Δabc and δxyz are similar triangles. if bc = x + 7, ac = x + 6, yz = 4 − x, and xz = 3 − x, find the value of x. a) − 2 3 b) − 3 2 c) 3 2 d) 2 3

Given ΔABC and ΔXYZ are similar triangles. BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x.

Similar triangles have sides in proportion.

Substituting the given values :

To solve for x we cross multiply

(x+7)(3-x)=(4-x)(x+6)

Using FOIL to multiply

Simplifying like terms

-4x+21=-2x+24

To solve for x we isolate the x term

Adding 2x both sides:

-4x+2x+21=24

-2x+21=24

Subtracting 24 both sides

-2x=24-21

-2x=3

Dividing by -2 we have x=

Option B is the right answer.