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 170 and the length of $overline{bc}$ is 850. in triangle xyz, the length of $overline{yz}$ is 60. what is the length of $overline{xy}$? a 204 b 182 c 60 d 12

Explanation:

Step1: Set up proportion

Since $\triangle ABC\sim\triangle XYZ$, we have $\frac{AB}{XY}=\frac{BC}{YZ}$. Let $XY = x$. Then $\frac{170}{x}=\frac{850}{60}$.

Step2: Cross - multiply

Cross - multiplying gives us $850x=170\times60$.

Step3: Solve for x

First, calculate $170\times60 = 10200$. Then $x=\frac{10200}{850}=12$.

Answer:

D. 12