Предмет: Геометрия, автор: Ourus7

Найдите площадь прямоугольного треугольника, у которого проекции катетов на гипотенузу равны 2 см и 18 см

Ответы

Автор ответа: matilda17562
20

Ответ:

60 см² .

Объяснение:

1) Высота, опущенная из вершины прямого угла на гипотенузу, есть среднее пропорциональное между проекциями катетов. В нашем случае

СH = √AH · BH = √(2·18) = √36 = 6 (см).

2) Сама гипотенуза АB = AH + BH = 2 + 18 = 20 (cм).

3) S  = 1/2 · AB · CH = 1/2 · 20 · 6 = 60 (см²).

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