Предмет: Математика, автор: fagdero

Можно ли из 4 палочек длины 1 см, 4 палочек Длины 2 см, 7 палочек длины 3 см и 5 палочек длины 4 см сложить прямоугольник? (Использовать нужно все палочки, разламывать их нельзя.)

Ответы

Автор ответа: kevraa

0

Ответ:

Поскольку палочки ломать нельзя, то каждая сторона прямоугольника измеряется целым числом сантиметров. Но тогда т.к. каждая сторона прямоугольника в его периметре участвует дважды, периметр выражается четным числом сантиметров. Посчитаем периметр: 4·1 + 4·2 + 7·3 + 5·4 = 4 + 8 + 21 + 20 = 53 — нечетное число. Значит, такого быть не могло.

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