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 4.8 inches and the length of segment CR is 7.2 inches. The distance between A and C is 9.6 inches.

What is the distance between the endpoints of the beams P and Q?

7.2 inches

3.6 inches

6.4 inches

12.0 inches

Answer 1

The answer is C, 6.4 inches

Explanation:

Answer 2

we will use Thalès theorem
since triangle PRQ and ARC are similar
PR = QR = PQ
AR CR AC
so we can use
PR = PQ
AR AC
but AR = CR finally, PQ = AC x PR / CR

PQ = 9.6 x 4.8 / 7.2 = 6.4

the true answer is 6.4 inches