Question

In the figure, FG is parallel to IJ. If FH = 12, HJ = 3, and the perimeter of triangle HIJ = 13, then what is the perimeter of triangle HGF?http://cdn.activelms.com/data/042c73b1-ddf5-4fd6-91e7-6c8434228f3d/Geometry%20Images/unit%207-5%20q2.png
a) 52
b) 48
c) 25
d) 36

Answer 1

Is D)36 correct?

Answer 2

lets see...

Answer 3

So I just separated the triangles.

Answer 4

If you look at lines FJ and GI, you can see that they are congruent to each other.

Answer 5

Therefore, if FH=12, then GH =12. And if HJ = 3, then HI = 3 too.

Answer 6

They have already given to us the perimeter of triangle HIJ, which is 13. We already have two of the three side lengths and we need to find the third one.
\(3 + 3 + x = 13\)
\(x = 7\)

Answer 7

Do you understand the process so far? @ellamoyseyuk

Answer 8

yes

Answer 9

OK. Now compare side HI with HF and HJ with HG. What is the relationship between those side lengths?

Answer 10

they are corresponding to each other

Answer 11

Well yes they are in the same position. But what can you do with 3 to get to 12?

Answer 12

times it by 4

Answer 13

good. so it means that these triangles are similar to each other

Answer 14

So would it be a) 52

Answer 15

yup!

Answer 16

thank you so much

Answer 17

yw