Question

Find the length of ad in the diagram shown

Answer 1

The answer to this is 7.5.

Answer 2

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

$\frac{AB}{AC} = \frac{AE}{AD}$

Now let AE = x

So plugging all the values we get

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

$\frac{5}{11} =\frac{x}{x+9}$

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