The two triangles are similar. What is the value of x in the figure below?

Solution:

Representing the triangle we have:

Since the two triangles △EBD and △ACD are similar we can write the following expressions:

BD/DC = ED/AD

BD/DC = ED/(AE + ED)

(2x - 2)/3x = 8/(6 + 8)

(2x - 2)/3x = 8/14

(2x -2) × 14 = 8 × 3x

28x - 28 = 24x

28x - 24x = 28

4x = 28

x = 7

The two triangles are similar. What is the value of x in the figure below?

Summary:

Since the two triangles are similar the value of x = 7