Question

In the diagram, BC⎯⎯⎯⎯⎯∥DE⎯⎯⎯⎯⎯ .

Answer 1

The length of AE is $18in$

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,

$\frac{EC}{DB} =\frac{AE}{AD}$

Substituting the values of the sides from the image, we get,

$\frac{3}{1} =\frac{AE}{6}$

Multiplying both sides of the equation by 6, we get,

$6(3)=AE$

Multiplying, we have,

$18=AE$

Thus, the length of AE is $18in$