1988 AHSME Problems/Problem 2

Problem

Triangles $ABC$ and $XYZ$ are similar, with $A$ corresponding to $X$ and $B$ to $Y$ . If $AB=3, BC=4$ , and $XY=5$ , then $YZ$ is:

$\text{(A)}\ 3\frac{3}{4} \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 6\frac{1}{4} \qquad \text{(D)}\ 6\frac{2}{3} \qquad \text{(E)}\ 8$

Solution

Since the triangles are similar, we know that the corresponding sides of the triangle are in ratio to each other. We have $\frac{\overline{AB}}{\overline{XY}}=\frac{\overline{BC}}{\overline{YZ}}$ . Plugging in values we have: $\frac{3}{4}=\frac{5}{\overline{YZ}}$ . Solving for $\overline{YZ}$ , we have $\overline{YZ}=6\frac{2}{3}$ . So, the answer is $\boxed{\text{D}}$ .

1988 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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1988 AHSME Problems/Problem 2

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