Question

question 8 (multiple choice worth 1 points) (03.05r mc) δabc is similar to δaxy by a ratio of 5:3. if bc = 25, what is the length of xy? diagram of triangles ( \triangle abc ) and ( \triangle axy ) with points ( a, b, c, x, y ) options: ( xy = 5 ); ( xy = 15 ); ( xy = 75 ); ( xy = 125 )

Explanation:

Step1: Recall the property of similar triangles

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

Step2: Substitute the known value and solve for XY

We know $BC = 25$, substitute into the ratio: $\frac{25}{XY}=\frac{5}{3}$. Cross - multiply to get $5\times XY=25\times3$. Then $5XY = 75$. Divide both sides by 5: $XY=\frac{75}{5}=15$.

Answer:

XY = 15 (corresponding to the option "XY = 15")