Question

If x = 37.5, solve for z using geometric mean. Round your answer to the nearest tenth if necessary.

Answer 1

ANSWER

z = 22.5

EXPLANATION

We want to use the geometric mean theorem to find the value of z.

The geometric mean theorem for similar triangles states that:

$\frac{z}{x}\text{ = }\frac{x\text{ - 24}}{z}$

This is gotten by equating the ratio of corresponding sides of similar triangles.

This implies that:

$\begin{gathered} \text{Cross}-mu\text{ltiplying:} \\ z\cdot\text{ z = x(x - 24)} \\ \Rightarrow z^2\text{ = 37.5(37.5 - 24)} \\ z^2\text{ = 37.5 }\cdot\text{ }13.5\text{ = }506.25 \\ z\text{ = }\sqrt[]{506.25} \\ z\text{ = }22.5\text{ } \end{gathered}$

That is the value of z.