The length of AE is [tex]18in[/tex]
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,
[tex]\frac{EC}{DB} =\frac{AE}{AD}[/tex]
Substituting the values of the sides from the image, we get,
[tex]\frac{3}{1} =\frac{AE}{6}[/tex]
Multiplying both sides of the equation by 6, we get,
[tex]6(3)=AE[/tex]
Multiplying, we have,
[tex]18=AE[/tex]
Thus, the length of AE is [tex]18in[/tex]
