Question

triangle uvw is similar to triangle xyz. find the measure of side zx. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since \(\triangle UVW\sim\triangle XYZ\), the ratios of corresponding sides are equal. Let \(ZX = x\). The proportion is \(\frac{ZX}{WU}=\frac{ZY}{WV}\).

Step2: Substitute values

Substitute \(WU = 2\), \(WV=3\), and \(ZY = 13.5\) into the proportion: \(\frac{x}{2}=\frac{13.5}{3}\).

Step3: Solve for \(x\)

Cross - multiply: \(3x=2\times13.5\). Then \(3x = 27\), so \(x=\frac{27}{3}=9\).

Answer:

\(9\)