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 :

$\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}$

so

$\frac{2}{4} = \frac{x+5}{5x-2} = \frac{x+7}{XZ}$ 

from 


$\frac{2}{4} = \frac{x+5}{5x-2}$

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

10x-4=4x+20

10x-4x=20+4

6x=24

x= 4 (units)