Question

a wire in the form of an equilateral triangle of area 36 root 3 square cm is straightened and then transformed into a square.find the area enclosed by the square.

Answer 1

Formulas related to the question :


$\boxed{Area \: \: of \: \: equilateral \: \: triangle = \frac{\sqrt{3}}{4} \times side^{2}} \\ \boxed{ Area \: \: of \: \: square = side^{2}} \\ \boxed{Perimeter \: \: o f \: \: equilateral \: \: triangle = 3 \times side } \: \\ \boxed{ Perimeter \: \: of \: \: square = 4 \times side}$




$\mathbf{Solution : }$




Given that the Area of equilateral triangle is 36√3 cm²




Area of equilateral triangle = 36√3 cm²

$= > \frac{ \sqrt{3} }{4} \times {side}^{2} = 36 \sqrt{3} \: {cm }^{2} \\ \\ \\ \\ = > \frac{1}{4} \times {side}^{2} = 36 \: {cm {}^{2} }^{} \\ \\ \\ \\ = > {side}^{2} = 36 \: cm {}^{2} \times 4 \\ \\ \\ \\ = > {side}^{2} = 6 \times 6 \times 2 \times 2 {cm}^{2} \\ \\ \\ \\ = > side = \sqrt{6 \times 6 \times 2 \times 2 \: \times cm \: \times cm} \\ \\ \\ \\ = > side = 6 \times 2 \: cm \\ \\ \\ \\ = > side = 12 \: cm$




So, the length of side of equilateral triangle is 12 cm





Perimeter of equilateral triangle or total length of the wire = 3( side )


Perimeter of equilateral triangle or total length of the wire = 3 ( 12 ) cm


Perimeter of equilateral triangle or total length of the wire = 36 cm





Total length cant be changed whether it will be triangle of a Square.



So, perimeter of equilateral triangle = perimeter of square


= > 36 cm = 4 × side of square


= > 36 cm / 4 = side of square


= > 9 cm = side of square


$\bold{ \underline{Hence, \: the \: side \: of \: square \: will \: be \: 9 \: cm}}$




Area of square = side²

Area of square = ( 9 cm )²

Area of square = 81 cm²

Answer 2

hope it help

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