Question

if $\triangle ayb\sim\triangle xyz$, $ab = 5$, $ay = 12$, and $ay = ax$, what is the length of $yz$? (1 point) $yz=\square$

Explanation:

Step1: Determine the ratio of similarity

Since \( \triangle AYB\sim\triangle XYZ\) and \(AY = AX = 12\), then \(XY=AY + AX=12 + 12=24\). The ratio of similarity is \(\frac{AY}{XY}=\frac{12}{24}=\frac{1}{2}\).

Step2: Use the ratio to find \(YZ\)

We know that \(\frac{AB}{YZ}=\frac{AY}{XY}\). Given \(AB = 5\) and \(\frac{AY}{XY}=\frac{1}{2}\), we can set up the equation \(\frac{5}{YZ}=\frac{1}{2}\). Cross - multiplying gives \(YZ=5\times2\).

Answer:

\(10\)