Perimeter of a square and an equilateral tria | vedclass

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Question

(A) For a square,the diagonal is given by $d = a \sqrt{2}$,where $a$ is the side length.Given $d = 12 \sqrt{2} 	ext{ cm}$,so $a = 12 	ext{ cm}$.The

Vedclass · Accepted Answer

$64 \sqrt{3} 	ext{ cm}^2$

Vedclass · Answer

(A) For a square,the diagonal is given by $d = a \sqrt{2}$,where $a$ is the side length.Given $d = 12 \sqrt{2} 	ext{ cm}$,so $a = 12 	ext{ cm}$.The perimeter of the square is $P = 4a = 4 	imes 12 = 48 	ext{ cm}$.Since the perimeter of the equilateral triangle is equal to the perimeter of the square,the perimeter of the triangle is $48 	ext{ cm}$.Let the side of the equilateral triangle be $s$. Then $3s = 48 	ext{ cm}$,which gives $s = 16 	ext{ cm}$.The area of an equilateral triangle is given by $\frac{\sqrt{3}}{4} s^2$.Area $= \frac{\sqrt{3}}{4} 	imes (16)^2 = \frac{\sqrt{3}}{4} 	imes 256 = 64 \sqrt{3} 	ext{ cm}^2$.

Perimeter of a square and an equilateral triangle is equal. If the diagonal of the square is $12 \sqrt{2} \text{ cm}$,then find the area of the equilateral triangle.

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