Find the length of ad in the diagram shown

Let as consider two triangles ABE and ACD

As we can see these two triangles ABE and ACD are similar triangles

Hence the ratio of sides must be equal

So

Now let AE = x

So plugging all the values we get

AB= 5 , AC= 11 , AE =x , AD = x+9

Cross multiplying we get

5(x+9) = 11(x)

Simplifying

5x +45 = 11x

Subtract 5x from both sides

45 = 6x

Divide both sides by 6

x= 45/6 = 7.5

Hence AE = 7.5

But we have to find the length of AD

AD = AE+ED = 7.5 + 9 = 16.5

AD= 16.5

Option D is the answer

a is the correct