Question

1. in △xyz, ∠xyz = 90°, and yw is the altitude to xz. if xw = 9 and wz = 16, what is the value of xz? a. 35 b. 25 c. 20 d. 30

Explanation:

Step1: Use the geometric mean theorem

In a right - triangle \( \triangle XYZ\) with altitude \(YW\) to the hypotenuse \(XZ\), we know that \(YW^{2}=XW\times WZ\) (not needed here). But for the length of the hypotenuse \(XZ\), we use the formula \(XZ = XW+WZ\).

Step2: Substitute the given values

Given \(XW = 9\) and \(WZ = 16\). Then \(XZ=9 + 16\).

Answer:

\(25\) (Option b)