Question

Prove that the area of an equilateral triangle described on one side of a square

is equal to half of the area of the equilateral triangle described on one of its

diagonal.​

Answer 1

$\mathbb\green{GIVEN}$

Equilateral triangle ABE is on AB of square ABCD.Equilateral triangle ACF is on diagonal AC.

$\mathbb\green{TO\:PROOVE}$

To proove:The area of an equilateral triangle described on one side of a square is equal to half of the area of the equilateral triangle described on one of its diagonal.

$\mathbb\green{PROOF}$

$= abe = \frac{1}{2} \times ar(acf) \\ = \frac{ar(abe)}{ar(acf)} = \frac{ {ab}^{2} }{ {ac}^{2} } (th.6) \\ = \frac{ {ab}^{2} }{ {ab}^{2} + {bc}^{2} } \\ by \: pythagoras \: therom \\ \frac{ {ab}^{2} }{2 {ab}^{2} } \\ ab = ac \: sides \: of \: square \\ = \frac{1 \times {ab}^{2} }{2 \times {ab}^{2} } \\ = \frac{ar(abe)}{ar(acf)} = \frac{1}{2}$

$\huge\mathbb{\green{ドラえもんバツ のび太}}$

Answer 2

Answer:

Refer the attachment for answer!

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