154k views
5 votes
What is the length of PR?

What is the length of PR?-example-1

2 Answers

6 votes

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

User Hassan Saqib
by
8.6k points
2 votes

Answer: C. 6

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


(PR)/(PQ)=(AC)/(AB)\\\\\Rightarrow\ (x)/(5)=(24)/(20)\\\\\Rightarrow\ x=(5*24)/(20)\\\\\Rightarrow\ x=6

Hence, the length of PR = 6 units.

User Ger Groot
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories