Triangle FGHFGHF, G, H is similar to triangle PQRPQRP, Q, R. Solve for y F is 10 G is 7 H is 6 P is 5 Q is 3.5 and R is y

Question

What is the answers to this question for solving similar triangles

 

Answer 1

Hi Alex,

 

I am thinking some figure would help us here.  

 

Are you saying this:

 

ΔFGH ˜ ΔPQR

 

So when you say to solve for y, which segment is y shown on?

 

I am assuming you mean that the segment FG = 10, and the segment GH=7, and HF = 6

And the segment PQ=5 and the segment QR is 3.5, and RP is "y".

 

IF this is the case (I am sorry, it is hard to tell from your description), then

 

FG        GH       HF

---  =  ---- =  ----

PQ        QR       RP

 

 

So first find FG/PQ = 10/5 = 2

 

And find  GH/QR = 73/5 = 2

 

Now, knowing that those fractions = 2, you can set up the proportion:

 

2 = HF/RP   or    2 = 6/y

 

So if y=3, then 6/y = 6/3 = 2, just like the other ratios, and so the answer is y = 3