Question

If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar (ΔABC) : ar (ΔBDE).

Answer 1

Given: (1) ΔABC is equilateral triangle.

(2) ΔBDE is equilateral triangle.

(3) D is the midpoint of BC.

To find:

PROOF : Let us draw the figure as per the instruction given in the question.

We know that area of equilateral triangle = , where a is the side of the triangle.

Let us assume that length of BC is a cm.

This means that length of BD is cm, Since D is the midpoint of BC.

------(1)

------(2)

Now, ar(ΔABC) : ar(ΔBDE) = (from 1 and 2)

=

Hence we get the result ar(ΔABC) : ar(ΔBDE) =