Q2 of 42 Page 214

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

Need to prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal


⇒ Let us take a square with side ‘a’


⇒ Then the diagonal of square will be a√ 2


⇒ Area of equilateral triangle with side ‘a’ is


⇒ Area of equilateral triangle with side a√2 is


⇒ Ratio of two areas can be given as follows


⇒


Hence proved


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