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)
15 yards
12 yards
25 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 \(\frac{XY}{AY}=\frac{YZ}{YB}\).

Step2: Substitute the given values

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

Step3: Solve for \(YB\)

Cross - multiply: \(24\times YB=8\times30\). Then \(24YB = 240\). Divide both sides by 24: \(YB=\frac{240}{24}=10\) yards.

Answer:

10 yards