prove that the area of an equilateral triangle on one side of a square is equal to half the area of the equilateral triangle describe on one of its diagonals.
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Let, side of square =a
Diagonal=√2 a
Area of triangle with side 'a'=>
A=(√3 /4)×a²
Similarly, area of triangle with side √2a=>
A'=(√3 /4) ×(√2a)²
=(√3 /4) ×2 ×a2
=2 {(√3 /4) ×a²}
=2A
A'=2A [Proved]
Diagonal=√2 a
Area of triangle with side 'a'=>
A=(√3 /4)×a²
Similarly, area of triangle with side √2a=>
A'=(√3 /4) ×(√2a)²
=(√3 /4) ×2 ×a2
=2 {(√3 /4) ×a²}
=2A
A'=2A [Proved]
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