In an equilateral triangle ABC,D  is a point on the side BC , such that  . Prove that

The correct answer is: Hence proved

Solution :-
Aim  :- Prove that 
Hint :- let the side of equilateral triangle be x , then we get height of equilateral
triangle as   .Now , Find length of DE and apply pythagoras theorem in
Right angle triangle ADE to find length of AD in terms of AB.
Explanation(proof ) :-
In equilateral triangle all sides are equal
Let , AB = BC =  CA  = x
Given BD = ⅓ BC = x/3
In equilateral triangle ,the altitudes and medians coincide
so,AE is median also i.e E is midpoint of BC 
BE = x/2
From diagram ,DE = BE - BD
We get height of equilateral triangle when side x is
Applying pythagoras theorem on triangle ADE
We get 


Substitute x by AB as x = AB

Hence proved