Діагоналі ромба дорівнюють 16 см і 30 см. Знайдіть площу чотири­кутника, вершинами якого є середини сторін даного ромба.

Гипотенуза в квадрате равна сумме квадратов катетов, т.е. 25=25x, x=1.
А отношение было 3x:4x, сл-но стороны 3 и 4. 
Если это прямоугольный треугольник, то высота делит гипотенузу на некоторые отрезки.
Высота это линия из прямого угла пересекающая гипотинузу под прямым углом. Рисуем ее. Получается два смежных прямоугольных треугольника: первый - гипотенуза 4 см, один катет наша высота- назовем ее Х, второй катет - часть гипотенузы нашего самого первого треугольника, назовем его У; и второй треугольник - его гипотенуза 3 см, один катет опять наша высота Х, второй - оставшаяся часть гипотенузы исходного треугольника она будет 5-y

Составляем квадратные уравнения:
x^2+y^2=9
x^2+(5-y)^2=16; x^2+25-10y+y^2=3; из первого равенства x^2+y^2=9 делаем подстановку, получаем: 9+25-10y=16; y=1,8

Подставляем в первое x^2+y^2=9
x^2= 9 - 1,8^2
x^2= 5.76
x=2.4

Сл-но высота равна 2,4 или 24\10=12\5

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