Maths-

General

Easy

Question

# 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

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