Given ΔABC ~ ΔPQR, what is the value of z?

A.
10 mm

B.
14 mm

C.
16.8 mm

D.
33.6 mm

Question

Given ΔABC ~ ΔPQR, what is the value of z?
  

 
 A.
10 mm
 
 B.
14 mm
 
 C.
16.8 mm
 
 D.
33.6 mm

logan13 · Answer

https://static.k12.com/calms_media/media/1572000_1572500/1572067/1/fc0054c0e4ceeaaa3bcb4d663e59230932df950e/MS_IMC-141210-110206.jpg

seratul · Answer

For this question, you should make a proportion. Which two side lengths are given in both triangles?

jabez177 · Answer

It deals with scale factor. We need to find the scale factor first.

logan13 · Answer

ok so would it be B

seratul · Answer

Keep in mind we need to find side lengths, not angles.

jabez177 · Answer

CB and RQ look the same, right?

logan13 · Answer

yes

jabez177 · Answer

Right. So in order to find out Scale Factor we have to divide 12 by 5.
What is $$12\div5$$?

logan13 · Answer

2.4

jabez177 · Answer

Right. 
Our Scale Factor is 2.4 so we can multiply the small triangle with a number on it and it will give us the length of the line on the bigger triangle.

jabez177 · Answer

So they want us to find the length of line Z, right?

logan13 · Answer

Yea

jabez177 · Answer

So CA and RP are similar. CA is 14 and to find RP or line Z, we have to multiply using our scale factor.

jabez177 · Answer

14 x 2.4

logan13 · Answer

33.6

jabez177 · Answer

Bingo! :)