In △ABC, ∠B = 90°, If the points D and E are on the side BC such that BD = DE = EC then which of the following is true?

8AE² = 3AC² + 5AD²

It is given that :- BD = DE = EC

In triangle ABC

h² = b² + p²

AC² = AB² + BC²

AC² = AB² + (3BD)²   ----(1)

In triangle ABE ,

AE² = AB² + BE²

AE² = AB² + ( 2BD)²    ----(2)

In triangle ABD,

AD² = AB² + BD²    ----(3)

Multiply equation 2 by 8

8AE² = 8AB² + 32BD²   ----(4)

Multiply equation 1 by 3 and equation 2 by 5 , and then add

3AC² + 5AD² = 8AB² + 32BD²   ----(5) 

On comparing equation 4 and 5,

8AE² = 3AC² + 5AD²