Question

What is the length of PR?

Answer 1

Answer: C. 6

Step-by-step explanation:

In the given picture , we have two triangles ΔABC and ΔPQR in which

∠B=∠Q=75° and ∠C=∠R=55°

By AA-Similarity postulate ΔABC ≈ ΔPQR.

We know that the corresponding sides of two similar triangles are proportional.

Therefore , we have

$\dfrac{PR}{PQ}=\dfrac{AC}{AB}\\\\\Rightarrow\ \dfrac{x}{5}=\dfrac{24}{20}\\\\\Rightarrow\ x=\dfrac{5\times24}{20}\\\\\Rightarrow\ x=6$

Hence, the length of PR = 6 units.

Answer 2

the larger triangle has angles of 75° and 55°.

the smaller triangle has angles of 75° and 55°.

the triangles are similar by AA.

$\bf \cfrac{smaller}{larger}\qquad \qquad \cfrac{PR}{AC}=\cfrac{PQ}{AB}\implies \cfrac{x}{24}=\cfrac{5}{20}\implies \cfrac{x}{24}=\cfrac{1}{4} \\\\\\ x=\cfrac{24}{4}\implies x=6$