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
[tex] \frac{AB}{AC} = \frac{AE}{AD} [/tex]
Now let AE = x
So plugging all the values we get
AB= 5 , AC= 11 , AE =x , AD = x+9
[tex] \frac{5}{11} =\frac{x}{x+9} [/tex]
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
