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?
Answer
A)3.2 inches
B)3.7 inches
C)4.2 inches
D)4.4 inches

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?
Answer
		A)3.2 inches
		B)3.7 inches
		C)4.2 inches
		D)4.4 inches

anonymous · Answer

attachment

anonymous · Answer

use ratio and proportion. .

i got 3.2

directrix · Answer

A)3.2 inches
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If Tri QRP ~ Tri ARC

RP/RC = QP/AC

3.7/5.6 = QP/4/9

You can do the crinkum-crankum work :)

PQ = 3.23 approx