Question

1. △yvh ~ △yba

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle YVH\sim\triangle YBA\), the ratios of corresponding sides are equal. That is \(\frac{YV}{YB}=\frac{YH}{YA}\).

Step2: Calculate \(YV\)

\(YV = YB + BV=16 + 22=38\)

Step3: Set up the proportion

Substitute the values into the proportion \(\frac{YV}{YB}=\frac{YH}{YA}\), we get \(\frac{38}{16}=\frac{x + 17}{17}\)

Step4: Cross - multiply

\(38\times17=16\times(x + 17)\)

\(646=16x+272\)

Step5: Solve for \(x\)

\(16x=646 - 272\)

\(16x=374\)

\(x=\frac{374}{16}=\frac{187}{8}=23.375\)

Answer:

\(x = 23.375\)