Question

△qrs ~ △tuv. solve for x.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle QRS\sim\triangle TUV\), the ratios of their corresponding sides are equal. So, \(\frac{QS}{TV}=\frac{QR}{TU}\).

Step2: Substitute the known values

We know \(QS = 3\), \(TV=6\), \(QR = 5\), and \(TU=x\). Substituting these into the ratio \(\frac{QS}{TV}=\frac{QR}{TU}\), we get \(\frac{3}{6}=\frac{5}{x}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(3x=6\times5\). Then \(3x = 30\). Divide both sides by 3: \(x=\frac{30}{3}\).

Answer:

\(x = 10\)