Question

In the figure below, triangle ABC is similar to triangle PQR:

A right triangle ABC with right angle at B and base BC is drawn. Length of AB is 4, length of BC is 2. A similar right triangle; triangle PQR, which is triangle ABC enlarged and reflected across a horizontal line, is drawn near it. The right angle is at Q. Angle A is congruent to angle P and angle C is congruent to angle R. The length of QR is 12.

What is the length of side PQ?

48
24
40
18

Answer 1

The answer is 24.

Explanation:

Since side BC is equal to 2 and that side corresponds with side QR, and QR equals 12, we know that to get from 2 to 12, you must multiply by 6 to get this. So, now we know that side AB must correspond with side QP. If side AB equals 4, then 4 multiplied by 6 equals 24 which is the length of side PQ.