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
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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)
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)
pals1:
ok i understand thankyou
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