Question

What is AE ? Enter your answer in the box. _____units

Answer 1

`AE=20` units

Explanation:

We are told that `AB` and `CD` are parallel, and therefore `/_AEB` and `/_CED` are the same. This tells us that the two triangles are similar shapes.

In terms of similarity `AE=ED`, but not the values, just the parts of the triangle they belong to.

The left hand triangle is `10/4` times bigger than the right hand triangle. So, `10/4(x+3)=2x+10`

`(10x)/4+30/4=2x+10`

`30/4-10=2x-(10x)/4`

`30/4-(10*4)/(1*4)=(2x*4)/(1*4)-(10x)/4`

`30/4-40/4=(8x)/4-(10x)/4`

`-10/4=-(2x)/4`

`-10=-2x`

`x=5`

`AE=2x+10`

`AE=2(5)+10=10+10=20`