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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
User Larzan
by
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1 Answer

15 votes
15 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 Petantik
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