Question

10 POINTS!! PLEASE HELP ASAP!!

The polygons below are similar. Find the value of y.

Polygons ABCD and EFGH are shown. AB equals 6. BC equals 8. CD equals 10. AD equals x. EF equals y. FG equals 6. GH equals z. HE equals 12.

(IMAGE IS ATTACHED DOWN BELOW!!)

A) 4.5
B) 7.5
C) 12
D) 16

Answer 1

If the polygons are similar, then we can set up a similarity ratio using sides AB and EF and any other 2 sides where both side lengths are given. That appears to be true for sides BC and FG. Our similarity ratio would be this then, going from the bigger polygon stuff on top and the smaller polygon stuff on bottom:

$\frac{8}{6}=\frac{6}{y}$.

If we cross multiply we have 8y = 36 and divide both sides by 8 to get that y = 4.5. There you go!

Answer 2

The answer depends upon what you are trying to find the value of like value of y or value of z. The person above did give you the correct way to solve for the value of y which is 4.5 as the answer.

However, if you need to solve for the value of z, then use ratio of side BC/side FG = side CD/side GH, which is:

8/6=10/z (cross multiply) to get 8z=6*10 then divide both sides by 8 to solve for z. 8z/8=60/8 then z=7.5 .