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.
[tex] \frac{BC}{YZ} =\frac{AC}{XZ} [/tex]
Substituting the given values :
[tex] \frac{x+7}{4-x} =\frac{x+6}{3-x} [/tex]
To solve for x we cross multiply
(x+7)(3-x)=(4-x)(x+6)
Using FOIL to multiply
[tex] 3x-x^{2} +21-7x =4x+24-x^{2} -6x [/tex]
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=[tex] -\frac{3}{2} [/tex]
Option B is the right answer.
