Question

Triangle ABC is similar to triangle FGH. What is the value of x?

Answer 1

22.5 cm

Explanation:

AB/FG = BC/GH

9/13.5 = 15/x

cross-multiply:

9x = 202.5

x = 202.5/9

x = 22.5

Answer 2

22.5 cm

Explanation:

You can make a proportion of the sides of the two triangles: AB/FG = 9/13.5 = 1/1.5 = 2/3

You also can do the same thing with another set of two sides: AC/FH = 12/18 = 2/3.

Then, you know the proportion is 2/3 so you have BC/GH = 2/3 = 15/x

Solving:

`(2)/(3) = (15)/(x)`

multiply both sides by 3x

`2x = 45\\x = 22.5`