14.8k views
5 votes
If x = 37.5, solve for z using geometric mean. Round your answer to the nearest tenth if necessary.

If x = 37.5, solve for z using geometric mean. Round your answer to the nearest tenth-example-1

1 Answer

7 votes

ANSWER

z = 22.5

Step-by-step explanation

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

The geometric mean theorem for similar triangles states that:


(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.

User Luke Femur
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.