Question

Se r1 = 3 e r2 = 5 ,determine o valor de x:


Com cálculo,por favor.

Answer 1

$\frac{r_1}{r_2} = \frac{y}{y + r_1 + r_2} \\ \\ \frac{3}{5} = \frac{y}{y + 3 + 5} \\ \\ \frac{3}{5} = \frac{y}{y + 8} \\ \\ 3y + 24 = 5y \\ 2y = 24 \\ \\ y = 8$

$y^2 = x^2 + (r_1)^2 \\ 8^2 = x^2 + 3^2 \\ 64 = x^2 + 9 \\ x^2 = 64 - 9 \\ x^2 = 55 \\ x = \sqrt{55}$