Question

use the image to answer the question
if ( \triangle xyzsim\triangle ayb ), and ( overline{xy}=24 ) yards, ( overline{yz}=30 ) yards, and ( overline{ya}=8 ) yards, then what is the length of ( overline{yb} )?
(1 point)
12 yards
25 yards
15 yards
10 yards

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle XYZ\sim\triangle AYB\), the ratios of corresponding sides are equal. That is \(\frac{YA}{XY}=\frac{YB}{YZ}\).

Step2: Substitute the given values

We know that \(XY = 24\) yards, \(YZ=30\) yards, and \(YA = 8\) yards. Substituting these into \(\frac{YA}{XY}=\frac{YB}{YZ}\), we get \(\frac{8}{24}=\frac{YB}{30}\).

Step3: Solve for \(YB\)

Cross - multiply: \(24\times YB=8\times30\). Then \(YB=\frac{8\times30}{24}\). Simplify \(\frac{240}{24}=10\).

Answer:

10 yards