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

Solution:

The diagram above shows the two triangles △BCD and △ACE.

The two triangles are similar under the condition SAS which implies that two sides are proportional and one angle equal. The two pairs of sides that are proportional are CD and CE & CB and BA. The angle which is the same and is also common to both triangles is ∠ACD = ∠BCD = 90°.

As the two triangles △BCD and △ACE are similar we can therefore write :

4x + 2 / 3x  = 28 / 20

20(4x + 2) = 28(3x)

80x + 40 = 84x

40 = 84x - 80x

40 = 4x

x = 10

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

Summary:

As the two triangles are similar, the value of x = 10.