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 16, length of BC is 20. 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 80.

What is the length of side PQ?

Answer 1

64. If QR is 80 and BC is 20, then triangle PQR is 4 times larger than triangle ABC. AB is 16. 16*4=64. PQ is 64

Answer 2

As the triangles are similar, we must match the ratios between the sides:

$\dfrac{AB}{PQ}=\dfrac{BC}{QR}\Longrightarrow \dfrac{16}{PQ}=\dfrac{20}{80}\iff PQ=\dfrac{16\times80}{20}=16\times4\iff\\\\\boxed{PQ=64}$