Question

triangle xyz is similar to triangle pqr. solve for k. k =

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle XYZ\sim\triangle PQR\), the ratios of corresponding sides are equal. That is \(\frac{YZ}{QR}=\frac{XZ}{PR}\).

Step2: Substitute the known values

We know \(YZ = 10.5\), \(XZ=16.5\), \(PR = 5.5\), and \(QR=k\). Substituting into the proportion \(\frac{10.5}{k}=\frac{16.5}{5.5}\).

Step3: Cross - multiply

Cross - multiplying gives \(16.5k=10.5\times5.5\).

Step4: Solve for \(k\)

First, calculate \(10.5\times5.5 = 57.75\). Then \(k=\frac{57.75}{16.5}\).

$$k = 3.5$$

Answer:

\(3.5\)