Question

1. \\( delta x z w sim delta x y v \\), find the perimeter of \\( delta x z w \\).

Explanation:

Step1: Find the similarity ratio

The similarity ratio \(k\) of \(\triangle XZW\) and \(\triangle XYV\) is \(\frac{XW}{XV}\). Given \(XW = 32 + 40=72\) and \(XV = 40\), so \(k=\frac{72}{40}=\frac{9}{5}\).

Step2: Calculate the perimeter of \(\triangle XYV\)

The perimeter of \(\triangle XYV\) is \(P_{XYV}=40 + 28+30 = 98\).

Step3: Find the perimeter of \(\triangle XZW\)

Since the ratio of perimeters of similar triangles is equal to the similarity ratio. Let \(P_{XZW}\) be the perimeter of \(\triangle XZW\). Then \(P_{XZW}=P_{XYV}\times k\). Substitute \(P_{XYV} = 98\) and \(k=\frac{9}{5}\), we get \(P_{XZW}=98\times\frac{9}{5}=\frac{882}{5} = 176.4\).

Answer:

\(176.4\)