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?

2.02 inches

2.8 inches

2.5 inches

3.4 inches

Answer 1

@Kaitlyn_The_Math_wiz
the triangles QRP and ARC are similar:)
do you have any idea what should we do now?

Answer 2

Identify the "similar sides"
Establish a proportion

Answer 3

no, thats why i am asking the question loll. i have a feeling the answer is either 2.8 or 2.5?

Answer 4

4.2 in is similar to PQ
3.4 in. is similar to 5.1 (I think)

Answer 5

@Kaitlyn_The_Math_wiz if two triangles are similar then there corresponding sides are similar, here QRP and ARC are similar so
\[\frac{QR}{AR}\ \ =\frac{QP}{AC} \ \ =\frac{RP}{RC}\]
could you use these to find PQ?

Answer 6

idk?!

Answer 7

RP=PR=3.4
RC=5.1
AC=4.2
PQ=QP
\[\frac{QP}{AC} \ \ =\frac{RP}{RC}\]
\[\frac{PQ}{4.2} \ \ =\frac{3.4}{5.1}\]
I think now you could find PQ!

Answer 8

its 2.8!:D

Answer 9

@Kaitlyn_The_Math_wiz did you try?

Answer 10

yes!

Answer 11

what did you get for PQ?

Answer 12

2.8

Answer 13

good:D