Question -
Answer -
Given:┬а(1)╬ФABC is equilateral triangle.
(2) ╬ФBDE is equilateral triangle.
(3) D is the midpoint of BC.
To find:┬а
PROOF : Let us draw the figure as per theinstruction given in the question.
We know that area of equilateral triangle =┬а
, where┬аa┬аis the side of the triangle.
Let us assume that length of BC is┬аa┬аcm.
This means that length of BD is┬а
┬аcm, Since D is the midpointof BC.
------(1)
------(2)
Now, ar(├ДABC) : ar(├ДBDE) =┬а
┬а(from 1 and 2)
=
Hence we get the result ar(├ДABC) : ar(├ДBDE) =┬а