# If Abc and Bde Are Two Equilateral Triangles Such that D is the Mid-point of Bc, Then Find Ar (δAbc) : Ar (δBde). - Mathematics

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

#### Solution

Given: (1) ΔABC is equilateral triangle.

(2) ΔBDE is equilateral triangle.

(3) D is the midpoint of BC.

To find: ar (Δ ABC ) : ar (ΔBDE)

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

We know that area of equilateral triangle = sqrt(3)/4 xx a^2, 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 a/2 cm, Since D is the midpoint of BC.

∴ area of equilateral Δ ABC =sqrt(3)/4 xx a^2   ------(1)

area of equilateral ΔBDE = sqrt(3)/4 xx (a/2)^2 ------(2)

Now, ar(ΔABC) : ar(ΔBDE) = sqrt(3)/4 xx a^2 : sqrt(3)/4 xx (a/2)^2   (from 1 and 2)

= 4 : 1

Hence we get the result ar(ΔABC) : ar(ΔBDE) = 4 : 1

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 1 | Page 59