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 1.8 inches and the length of segment CR is 3.3inches. The distance between A and C is 6.6 inches.
What is the distance between the endpoints of the beams P and Q? (picture below)

A)0.9 inches
B)1.8 inches
C)2.5 inches
D)3.6 inches

Answer 1

Based on your question where as the ask of the problem is to get the distance between the end points of the beams P and Q base on the picture below and according to my calculation and step by step procedure i came up with an answer of D. 3.6 inches

Answer 2

`\boxed{\boxed{PQ=3.6\ in}}`

Explanation:

As it is given as ΔQRP and ΔARC are similar, so the ratio of their corresponding sides will be same.

So,

`(RC)/(PR)=(AC)/(PQ)`

It is given as,

RC = 3.3

PR = 1.8

AC = 6.6

PQ = ??

Putting the values,

`\Rightarrow (3.3)/(1.8)=(6.6)/(PQ)`

`\Rightarrow PQ=(6.6* 1.8)/(3.3)=3.6`