Question

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.

Answer 1

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.

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

Substituting the given values :

$\frac{x+7}{4-x} =\frac{x+6}{3-x}$

To solve for x we cross multiply

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

Using FOIL to multiply

$3x-x^{2} +21-7x =4x+24-x^{2} -6x$

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=$-\frac{3}{2}$

Option B is the right answer.

Answer 2

I believe the answer is B) -3/2 or -1.5.

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