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 3.4 inches and the length of segment CR is 5.1 inches. The distance between A and C is 4.2 inches

What is the distance between the endpoints of the beams P and Q?
Answer choices
2.02 inches
2.5 inches
2.8 inches
3.4 inches

Answer 1

Answer: 2.8 inches

Explanation:

Given : The beams intersect each other to form two similar triangles ΔQRP and ΔARC .

PR = 3.4 inches

CR = 5.1 inches.

AC = 4.2 inches

To find : PQ

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

i.e. for similar triangles ΔQRP and ΔARC , we have

`\Rightarrow (PQ)/(AC)=(PR)/(CR)\\\\\Rightarrow(PQ)/(4.2)=(3.4)/(5.1)\\\\\Rightarrow\ PQ=4.2*(3.4)/(5.1)=2.8\text{ inches}`

Hence, the distance between the endpoints of the beams P and Q = 2.8 inches

.

Answer 2

PR : RC = PQ : AC

so,

PQ = 2.8 inches

Hope this helps