Question

what is the value of x that makes the triangles similar?

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{PQ}{ST}=\frac{QR}{TU}\). Substituting the given values: \(\frac{8}{15}=\frac{12}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(8x = 15\times12\).

Step3: Solve for \(x\)

First, calculate \(15\times12 = 180\). Then, \(x=\frac{180}{8}=22.5\).

Answer:

\(22.5\)