Предмет: Алгебра, автор: Александриния

Помогите решить задачу, прошу!

Площадь прямоугольного треугольника равна`90 см`. Сумма площадей катетов квадратов, постороенных на его катетах, равна `369см`. Каковы катеты этого треугольника.

Ответы

Автор ответа: SashkaLi

0,5ab=90

a^2+b^2=369
(это системма)
a=180/b
теперь подставляем а:
(180/b)^2+b^2=369

b^4-369b^2+32400=0
(затем решаем уравнение, причем в >0)
b=15=> а=6

и b=12 => а=7.5

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