Question

unit test
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if △xyz ~ △ayb and yb = 25 ft, ya = 16 ft, and yz = 88 ft, then what is the length of yx?
55.32 ft
137.5 ft
67.6 ft

Explanation:

Step1: Identify Similar Triangles

Since \(\triangle XYZ \sim \triangle AYB\), their corresponding sides are proportional. So, \(\frac{YX}{YA}=\frac{YZ}{YB}\).

Step2: Substitute Known Values

We know \(YB = 25\) ft, \(YA = 16\) ft, and \(YZ = 88\) ft. Let \(YX = x\) (the length we need to find). Substituting into the proportion: \(\frac{x}{16}=\frac{88}{25}\).

Step3: Solve for \(x\)

Cross - multiply: \(25x=16\times88\). Calculate \(16\times88 = 1408\). Then \(x=\frac{1408}{25}=56.32\) ft.

Answer:

\(56.32\) ft