Question

Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 3.7 inches and the length of segment CR is 5.6 inches. The distance between A and C is 4.9 inches. What is the distance between the endpoints of the beams P and Q?

A) 3.2 inches.
B) 3.7 inches.
C) 4.2 inches.
D) 4.4 inches.

Answer 1

A) 3.2 inches

Explanation:

look at the other answer if you need an explanation but here's proof its correct

Answer 2

We know that QRP and ARC are similar.
Therefore:
x : 3.7 = 4.9 : 5.6
5.6 x = 3.7 * 4.9
5.6 x = 18.13
x = 18.13 : 5.6
x = 3.2375
PQ ≈ 3.2
Answer:
A ) 3.2 inches