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А как вам такое решениеце? Высота к гипотенузе делит прямоугольный треугольник на два, ему же подобных (и подобных между собой, конечно) Поскольку в этих треугольниках оба катета исходного треугольника играют роль гипотенузы, площади этих треугольников отностятся как квадраты катетов (в данном случае - соответственных сторон)
S1/S2 = (6/8)^2 = 9/16;
В сумме S1 + S2 = 8*6/2 = 24;
Остюда очень легко найти S1, S2 и их разность :)
Вот один из Пусть S1 = 9x; S2 = 16x, где х - неизвестная величина.
Тогда S1 + S2 = 25x = 24; x = 24/25;
S2 - S1 = (16 - 9)*x = 7*24/25 = 6,72;
