Question

(03 05r mc)
△abc is similar to △axy by a ratio of 5:3. if bc = 25, what is the length of xy?
options: xy = 5; xy = 15; xy = 75; xy = 125

Explanation:

Step1: Recall Similar Triangles Ratio

For similar triangles, the ratio of corresponding sides is equal. Given $\triangle ABC \sim \triangle AXY$ with ratio $5:3$, so $\frac{BC}{XY}=\frac{5}{3}$.

Step2: Substitute Known Value

We know $BC = 25$. Let $XY = x$. Then $\frac{25}{x}=\frac{5}{3}$. Cross - multiply: $5x=25\times3$.

Step3: Solve for \(x\)

Simplify the right - hand side: $5x = 75$. Divide both sides by 5: $x=\frac{75}{5}=15$.

Answer:

\(XY = 15\)