Предмет:
МатематикаАвтор:
анонимВведем переменную.
Пусть m - длина проекции одного катета прямоугольного треугольника, тогда (4 * m) - проекция второго катета на гипотенузу.
Найдем проекции катетов:
m + 4 * m = 20;
m = 4;
4 * m = 16;
Используем теорему Пифагора для двух треугольников, образованных высотой:
a^2 = h^2 + 16;
b^2 = h^2 + 256;
Теперь используем теорему Пифагора для большого треугольника:
(5 * m)^2 = a^2 + b^2;
400 = h^2 + 16 + h^2 + 256;
2 * h^2 = 400 - 272;
2 * h^2 = 128;
h^2 = 64;
h = 8 см.
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