Question

prove that area of the equilateral triangle described on the side of asquare is half the area of the equilateral triangles described on its diagonal

Answer 1

Let all the sides of the square and be X
Diagnol ac =root 2X
Now,
Sides of triangle PDC will be X unit each..
And sides of triangle AQC will be root 2x each..

Now,
ar(PDC) =root 3/4 x2.......... i
Ar(AQC) =root 3/4(root 2 x2)........ii

Now
Ar(PDC)/ ar(AQCA)=1/2 ( from i and ii)

Answer 2

plz refer to this attachment