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Guided Example #2 - Similar Triangles

Find the value of x in the following pair of triangles.

A.9

B. 10

C. 8

D. Cannot be determinated

Step 1

The correct answer is a.

$Δ A B C$ and

$Δ A D E$ are similar as they are equiangular.

Step 2

Therefore

$\frac{A D}{A B} = \frac{D E}{B C}$

$x + \frac{4}{x} = \frac{6}{3} = 2$

Step 3

Cross multiply and solve for x

$x + 4 = 2 x$

$2 x - x = 4$

$x = 4$

All Steps

The correct answer is a.

$Δ A B C$ and

$Δ A D E$ are similar as they are equiangular.

Therefore

$\frac{A D}{A B} = \frac{D E}{B C}$

$x + \frac{4}{x} = \frac{6}{3} = 2$

Cross multiply and solve for x

$x + 4 = 2 x$

$2 x - x = 4$

$x = 4$