Olimpiadas matemáticas:@0.107368:0.074738:0.438969:0.074738:0.438969:0.046697:0.107368:0.046697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
166:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
1. :@0.096359:0.125354:0.115100:0.125354:0.115100:0.108218:0.096359:0.108218:0.000000:0.000000:0.000000
Ricardo quería cortar un pedazo de madera en nueve pedazos de la misma longitud y marcó los puntos :@0.124848:0.125354:0.907562:0.125354:0.907562:0.109684:0.124848:0.109684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde debía cortar. Luciana quería cortar el mismo pedazo de madera en solo ocho pedazos de la misma :@0.124848:0.141951:0.907798:0.141951:0.907798:0.126281:0.124848:0.126281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
longitud y marcó los puntos donde debía cortar. Si el pedazo de madera se corta en todos los puntos que :@0.124848:0.158547:0.907726:0.158547:0.907726:0.142877:0.124848:0.142877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ambos marcaron, ¿cuántos pedazos de madera se obtendrán?:@0.124848:0.175143:0.579876:0.175143:0.579876:0.159474:0.124848:0.159474:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.199775:0.100174:0.199775:0.100174:0.182874:0.096359:0.182874:0.000000
Argumenta:@0.124848:0.199775:0.215346:0.199775:0.215346:0.182874:0.124848:0.182874:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215346:0.199775:0.219069:0.199775:0.219069:0.182639:0.215346:0.182639:0.000000
en tu cuaderno la solución.:@0.219069:0.199775:0.417680:0.199775:0.417680:0.184105:0.219069:0.184105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.343555:0.100266:0.343555:0.100266:0.326931:0.096359:0.326931:0.000000
Argumenta:@0.124848:0.343555:0.215346:0.343555:0.215346:0.326654:0.124848:0.326654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215346:0.343555:0.219069:0.343555:0.219069:0.326419:0.215346:0.326419:0.000000
en tu cuaderno la solución.:@0.219069:0.343555:0.417680:0.343555:0.417680:0.327885:0.219069:0.327885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.096359:0.539378:0.100266:0.539378:0.100266:0.522754:0.096359:0.522754:0.000000
Argumenta:@0.124848:0.539378:0.215346:0.539378:0.215346:0.522478:0.124848:0.522478:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.215346:0.539378:0.219069:0.539378:0.219069:0.522243:0.215346:0.522243:0.000000
en tu cuaderno la solución.:@0.219069:0.539378:0.417680:0.539378:0.417680:0.523709:0.219069:0.523709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.096359:0.242760:0.115100:0.242760:0.115100:0.225624:0.096359:0.225624:0.000000:0.000000:0.000000
El gráfico muestra dos rectángulos cuyos lados son pa-:@0.124848:0.242760:0.535121:0.242760:0.535121:0.227090:0.124848:0.227090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ralelos. ¿Cuál es la diferencia de los perímetros de los dos :@0.124848:0.259356:0.539100:0.259356:0.539100:0.243686:0.124848:0.243686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
rectángulos?:@0.124848:0.275952:0.218792:0.275952:0.218792:0.260283:0.124848:0.260283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. :@0.096359:0.390647:0.115100:0.390647:0.115100:0.373511:0.096359:0.373511:0.000000:0.000000:0.000000
Dos segmentos, cada uno de 2 cm de largo, están marcados en lados opuestos de un cuadrado de lado 16 cm. :@0.124848:0.390647:0.907765:0.390647:0.907765:0.374977:0.124848:0.374977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los extremos de los segmentos se unen como se muestra en el diagrama. ¿Cuál es el área sombreada?:@0.124848:0.407244:0.856849:0.407244:0.856849:0.391574:0.124848:0.391574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. :@0.096359:0.594271:0.115100:0.594271:0.115100:0.577135:0.096359:0.577135:0.000000:0.000000:0.000000
Halla:@0.124848:0.594271:0.165426:0.594271:0.165426:0.577370:0.124848:0.577370:0.000000:0.000000:0.000000:0.000000:0.000000
 el área de la región sombreada en cada gráfico.:@0.165426:0.594271:0.514458:0.594271:0.514458:0.578601:0.165426:0.578601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a)   :@0.124848:0.617990:0.157063:0.617990:0.157063:0.600854:0.124848:0.600854:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.333799:0.617990:0.337522:0.617990:0.337522:0.600854:0.333799:0.600854:0.000000
 :@0.362292:0.617990:0.366014:0.617990:0.366014:0.600854:0.362292:0.600854:0.000000
 :@0.397907:0.617990:0.401630:0.617990:0.401630:0.600854:0.397907:0.600854:0.000000
           c):@0.458223:0.617990:0.513266:0.617990:0.513266:0.600854:0.458223:0.600854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b)   :@0.124867:0.760331:0.157082:0.760331:0.157082:0.743196:0.124867:0.743196:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.333818:0.760331:0.337540:0.760331:0.337540:0.743196:0.333818:0.743196:0.000000
 :@0.362310:0.760331:0.366033:0.760331:0.366033:0.743196:0.362310:0.743196:0.000000
 :@0.397926:0.760331:0.401648:0.760331:0.401648:0.743196:0.397926:0.743196:0.000000
           d):@0.458241:0.760331:0.515956:0.760331:0.515956:0.743196:0.458241:0.743196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.515956:0.760331:0.519992:0.760331:0.519992:0.744662:0.515956:0.744662:0.000000
4 m:@0.731142:0.246479:0.756707:0.246479:0.756707:0.232234:0.731142:0.232234:0.000000:0.000000:0.000000
6 m:@0.727792:0.314914:0.753356:0.314914:0.753356:0.300668:0.727792:0.300668:0.000000:0.000000:0.000000
6 m:@0.622637:0.283745:0.648201:0.283745:0.648201:0.269500:0.622637:0.269500:0.000000:0.000000:0.000000
8 m:@0.799844:0.283745:0.825408:0.283745:0.825408:0.269500:0.799844:0.269500:0.000000:0.000000:0.000000
16 cm:@0.550342:0.472779:0.591553:0.472779:0.591553:0.458534:0.550342:0.458534:0.000000:0.000000:0.000000:0.000000:0.000000
2 cm:@0.500973:0.429415:0.534009:0.429415:0.534009:0.415170:0.500973:0.415170:0.000000:0.000000:0.000000:0.000000
2 cm:@0.460767:0.516169:0.493803:0.516169:0.493803:0.501923:0.460767:0.501923:0.000000:0.000000:0.000000:0.000000
Adaptado de: http://www.ommenlinea.org:@0.673484:0.937536:0.903082:0.937536:0.903082:0.926139:0.673484:0.926139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.245599:0.736215:0.253775:0.736215:0.253775:0.721970:0.245599:0.721970:0.000000
2:@0.328507:0.675249:0.336682:0.675249:0.336682:0.661003:0.328507:0.661003:0.000000
8:@0.602196:0.614805:0.610371:0.614805:0.610371:0.600560:0.602196:0.600560:0.000000
9:@0.722813:0.614805:0.730988:0.614805:0.730988:0.600560:0.722813:0.600560:0.000000
5:@0.791498:0.655039:0.799673:0.655039:0.799673:0.640794:0.791498:0.640794:0.000000
3:@0.791498:0.699044:0.799673:0.699044:0.799673:0.684799:0.791498:0.684799:0.000000
8 cm:@0.296828:0.899415:0.329864:0.899415:0.329864:0.885170:0.296828:0.885170:0.000000:0.000000:0.000000:0.000000
2 cm:@0.168153:0.909159:0.201189:0.909159:0.201189:0.894914:0.168153:0.894914:0.000000:0.000000:0.000000:0.000000
3 cm:@0.426676:0.798567:0.459712:0.798567:0.459712:0.784322:0.426676:0.784322:0.000000:0.000000:0.000000:0.000000
5 cm:@0.426676:0.851374:0.459712:0.851374:0.459712:0.837129:0.426676:0.837129:0.000000:0.000000:0.000000:0.000000
12 cm:@0.634473:0.774142:0.675684:0.774142:0.675684:0.759896:0.634473:0.759896:0.000000:0.000000:0.000000:0.000000:0.000000
6 cm:@0.762746:0.831022:0.795782:0.831022:0.795782:0.816777:0.762746:0.816777:0.000000:0.000000:0.000000:0.000000
Se obtendrán 16 pedazos de madera.:@0.125443:0.211623:0.299593:0.211623:0.299593:0.201651:0.125443:0.201651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La diferencia es de 48 metros.:@0.125443:0.357624:0.262924:0.357624:0.262924:0.347653:0.125443:0.347653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El área sombreada es 16 cm .:@0.128023:0.552296:0.262925:0.552296:0.262925:0.542324:0.128023:0.542324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.257547:0.548448:0.260883:0.548448:0.260883:0.542634:0.257547:0.542634:0.000000
21:@0.380145:0.674314:0.391590:0.674314:0.391590:0.664343:0.380145:0.664343:0.000000:0.000000
56:@0.842047:0.661623:0.853492:0.661623:0.853492:0.651652:0.842047:0.651652:0.000000:0.000000
54 cm:@0.831680:0.826327:0.860528:0.826327:0.860528:0.816355:0.831680:0.816355:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.860533:0.822475:0.863869:0.822475:0.863869:0.816662:0.860533:0.816662:0.000000
40 cm:@0.421386:0.914818:0.450233:0.914818:0.450233:0.904846:0.421386:0.904846:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.450233:0.910969:0.453569:0.910969:0.453569:0.905155:0.450233:0.905155:0.000000