Question

PLEASE HELP

What is AE ?

Answer 1

Since segments AB and CD are parallel, the triangles are similar. That makes sides AB and CD corresponding sides. Sides AE and DE are also corresponding sides. In similar triangles, the lengths of corresponding sides are proportional meaning they are in the same ratio.

`(AB)/(CD) = (AE)/(DE)`

`(12)/(10) = (2x + 4)/(x + 8)`

Reduce the fraction on the left side.

`(6)/(5) = (2x + 4)/(x + 8)`

Cross multiply.

`6(x + 8) = 5(2x + 4)`

`6x + 48 = 10x + 20`

`-4x = -28`

`x = 7`

AE = 2x + 4 = 2(7) + 4 = 14 + 4 = 18

Answer: AE = 18