Question

What is the measure of x?
16
x=[?]
Give your answer in simplest form.

Answer 1

Answer: $8\sqrt{5}$

Step-by-step explanation:

By the geometric mean theorem,

$\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8$

Thus, by the Pythagorean thoerem,

$8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}$