Question

14 choose the appropriate value for x for the following similar triangles given below. △abc ~ △xyz. a y 20 z 50 x c b 40 a 30 b 100 c 25 d 60

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle ABC\sim\triangle XYZ\), the ratios of corresponding sides are equal.

Step2: Set up the proportion

\(\frac{BC}{YZ}=\frac{AB}{XY}\). Substitute \(BC = 40\), \(YZ=20\), \(AB = 50\), and \(XY=x\) into the proportion: \(\frac{40}{20}=\frac{50}{x}\).

Step3: Cross - multiply

\(40x=20\times50\).

Step4: Solve for \(x\)

\(40x = 1000\), then \(x=\frac{1000}{40}=25\).

Answer:

C. 25