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? (5 points)

Answer 1

yo

Answer 2

You can set up a proportion.

\(\dfrac{7.2}{4.8} = \dfrac{9.6}{x}\)

Now, can you cross multiply and solve?

Answer 3

7.2*z=7.2z znd 9.6*4.8=46.08 right?

Answer 4

so its\[\frac{ 46.08 }{ 7.2z }\]

Answer 5

right?

Answer 6

Almost. You multiplied correctly, but it should be:

\(46.08 = 7.2z\)

Now what's our next step?

Answer 7

and the answer is 6.4 right?

Answer 8

i divide to get 6.4

Answer 9

\(46.08 = 7.2z\)

Divide 7.2 to both sides:

\(\dfrac{46.08}{7.2} = \dfrac{7.2z}{7.2}\)

\(6.4 = \dfrac{\cancel{7.2}z}{\cancel{7.2}}\)

\(z = 6.4~ \Large\color{lime} \checkmark\)

Answer 10

Yep, you got it.

Answer 11

yay thx

Answer 12

No problem.