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?
Answer & explanation
Correct answer: option 3
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