Question

Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side ZX measures 4x – 2. Find the value of x.

Answer 1

`x=8`

Explanation:

In similar triangles, corresponding sides' ratio are equal.

• Side AB corresponds to Side XY
• Side BC corresponds to Side YZ
• Side CA corresponds to Side ZX

We can set up a ratio of
`(SideAB)/(Side XY)=(SideCA)/(Side ZX)`

Hence, we can write (and solve):

`(Side AB)/(Side XY)=(Side CA)/(SideZX)\\(2)/(4)=(x+7)/(4x-2)\\2(4x-2)=4(x+7)\\8x-4=4x+28\\8x-4x=28+4\\4x=32\\x=(32)/(4)=8`

So, x = 8