Question

The diagonal of a square is 4√3 cm and the area of an equilateral triangle is√3 Times the area of the square. What is the length of the side of the triangle?​

Answer 1

STEP-BY-STEP EXPLANATION:

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$Diagonal_{(Square)} = 4 \sqrt{3} \: \: \: ...(given)$

$\implies (Side \:of \: Square ) \sqrt{2} = 4 \sqrt{3}$

$\implies Side \: of \: Square = \frac{4 \sqrt{3}}{ \sqrt{2} }$

$\implies Side \: of \: Square = \frac{4 \sqrt{3}}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$\implies Side \: of \: Square = \frac{4 \sqrt{6}}{ {2} }$

$\implies Side \: of \: Square = 2 \sqrt{6}cm$

$Area_{(Square)} = (Side)^{2}$

$\implies Area_{(Square)} = (2 \sqrt{6} )^{2}$

$\implies Area_{(Square)} = 4 \times {6}$

$\implies Area_{(Square)} = 24 {cm}^{2}$

$Area_{(Equilateral \: ∆)} = \sqrt{3} \times Area_{(Square)} \: \: \: ...(given)$

$\implies Area_{(Equilateral \: ∆)} = \sqrt{3} \times 24 {cm}^{2}$

$\implies Area_{(Equilateral \: ∆)} = 24 \sqrt{3} {cm}^{2}$

$\implies \frac{ \sqrt{3} }{4} \times {(Side \: of \: Equilateral \: ∆)}^{2} = 24 \sqrt{3} {cm}^{2}$

$\implies {(Side \: of \: Equilateral \: ∆)}^{2} = 24 \cancel{\sqrt{3}} \times \frac{4}{ \cancel{\sqrt{3}} }$

$\implies {(Side \: of \: Equilateral \: ∆)}^{2} = 96 {cm}^{2}$

$\implies {Side \: of \: Equilateral \: ∆} = \sqrt{96 {cm}^{2}}$

$\implies {Side \: of \: Equilateral \: ∆} = 4\sqrt{6}cm$

REQUIRED ANSWER,

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• ${Side \: of \: Equilateral \: ∆} = 4\sqrt{6}cm$

Answer 2

Answer:

answer of this question is 8 cm .