Question

triangle abc is similar to triangle xyz, where a, b, and c correspond to x, y, and z, respectively. in triangle abc, the length of $overline{ab}$ is 140 and the length of $overline{bc}$ is 700. in triangle xyz, the length of $overline{yz}$ is 90. what is the length of $overline{xy}$?
a 252
b 158
c 90
d 18

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle XYZ$, we have $\frac{AB}{XY}=\frac{BC}{YZ}$. Let $XY = x$. Then $\frac{140}{x}=\frac{700}{90}$.

Step2: Cross - multiply

Cross - multiplying gives us $700x=140\times90$.

Step3: Solve for $x$

First, calculate $140\times90 = 12600$. Then $x=\frac{12600}{700}=18$.

Answer:

D. 18