The length of AE is ![18in](/tpl/images/0516/1939/62b23.png)
Explanation:
From the figure, we can see that the two triangles ΔAED and ΔACB are similar. Thus, the legs of the triangle are proportional to each other.
Thus, we have,
![\frac{EC}{DB} =\frac{AE}{AD}](/tpl/images/0516/1939/cab99.png)
Substituting the values of the sides from the image, we get,
![\frac{3}{1} =\frac{AE}{6}](/tpl/images/0516/1939/a1e22.png)
Multiplying both sides of the equation by 6, we get,
![6(3)=AE](/tpl/images/0516/1939/2e409.png)
Multiplying, we have,
![18=AE](/tpl/images/0516/1939/4eb92.png)
Thus, the length of AE is ![18in](/tpl/images/0516/1939/62b23.png)