Question

Помогите решить задачу срочно умоляю!(

Answer 1

Пусть a, b -- стороны прямоугольника, d -- диагональ.
$s = a times b \ {d}^{2} = {a}^{2} + {b}^{2} \ \ a times b = 48 \ {a}^{2} + {b}^{2} = 100 \ \ a times b = 48 \ {a}^{2} + 2ab + {b}^{2} = 100 + 2ab \ \ a times b = 48 \ {(a + b)}^{2} = 100 + 2 times 48 \ \ a times b =48 \ {(a + b)}^{2} = 196 \ \ a + b = 14 \ a times b = 48 \ \ b = 14 - a \ a(14 - a) = 48 \ \ b = 14 - a \ 14a - {a}^{2} = 48 \ \ b = 14 - a \ {a}^{2} - 14a + 48 = 0 \ \ d = {b}^{2} - 4ac = 196 - 4 times 48 = 4 \ a1 = frac{14 + 2}{2} = frac{16}{2} = 8 \ b1 = 14 - 8 = 6 \ \ a2 = frac{14 - 2}{2} = frac{12}{2} = 6 \ b2 = 14 - 6 = 8$
=> стороны равны 6 и 8.