Answer :

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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