Question

riangle 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 YZ measures 5x – 2. Find the value of x.

Answer 1

ABC is similar to XYZ means that the corresponding sides are proportional, that is :


`(AB)/(XY) = (BC)/(YZ) = (AC)/(XZ)`

so


`(2)/(4) = (x+5)/(5x-2) = (x+7)/(XZ)`

from



`(2)/(4) = (x+5)/(5x-2)`

2(5x-2)=4(x+5)

10x-4=4x+20

10x-4x=20+4

6x=24

x= 4 (units)