Question

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

Explanation:

Step1: Set up proportion

For similar triangles $\triangle ABC\sim\triangle XYZ$, the ratios of corresponding sides are equal. So, $\frac{AB}{XY}=\frac{BC}{YZ}$. Here, $AB = 50$, $XY=x$, $BC = 40$, and $YZ = 20$. The proportion is $\frac{50}{x}=\frac{40}{20}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{50}{x}=\frac{40}{20}$ gives $40x=50\times20$.

Step3: Solve for x

First, calculate $50\times20 = 1000$. Then, we have $40x = 1000$. Divide both sides by 40: $x=\frac{1000}{40}=25$.

Answer:

A. 25