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 ab is 140 and the length of bc is 700. in triangle xyz, the length of yz is 90. what is the length of xy?
a 352
b 158
c 90
d 18

Explanation:

Step1: Set up the proportion

Since \(\triangle ABC\sim\triangle XYZ\), the ratios of corresponding sides are equal. That is \(\frac{AB}{XY}=\frac{BC}{YZ}\).

Step2: Substitute the known values

We know \(AB = 140\), \(BC=700\), and \(YZ = 90\). Substituting into the proportion \(\frac{140}{XY}=\frac{700}{90}\).

Step3: Cross - multiply

Cross - multiplying gives us \(700\times XY=140\times90\).

Step4: Solve for \(XY\)

First, calculate \(140\times90 = 12600\). Then \(XY=\frac{12600}{700}\).
\(XY = 18\)

Answer:

D. 18