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# Solution - In an Equilateral Triangle Abc, D is a Point on Side Bc Such that Bd = 1/3bc . Prove that 9 Ad^2 = 7 Ab^2 - CBSE Class 10 - Mathematics

#### Question

In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3BC . Prove that 9 AD2 = 7 AB2

#### Solution

Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC.

∴ BE = EC = (BC)/2 = a/2

And, AE = (asqrt3)/2

Given that, BD = 1/3BC

∴ BD = a/3

DE = BE - BD = a/2 - a/3 = a/6

Applying Pythagoras theorem in ΔADE, we get

AD^2 = ((asqrt3)/2)^2 + (a/6)^2

= ((3a^2)/4) + (a^2/36)

= (28a^2)/36

= 7/9 AB^2

⇒ 9 AD2 = 7 AB2

Is there an error in this question or solution?

#### Reference Material

Solution for question: In an Equilateral Triangle Abc, D is a Point on Side Bc Such that Bd = 1/3bc . Prove that 9 Ad^2 = 7 Ab^2 concept: Pythagoras Theorem. For the course CBSE
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