Question

Find the value of x and y.

Answer 1

By the geometric mean theorem,

$\frac{y}{4}=\frac{12}{y} \\ \\ y^{2}=48 \\ \\ \boxed{y=4\sqrt{3}}$

So, by the Pythagorean theorem,

$12^{2}+(4\sqrt{3})^{2}=x^{2}\\\\144+48=x^{2}\\\\192=x^{2}\\\\\boxed{x=8\sqrt{3}}$