Question

find the area of an equilateral triangle whose area is 20√3 cm^2​

Answer 1

The question must be:

find the sides of an equilateral triangle whose area is 20√3 cm^2.

Answer :

Given:

area of an equilateral triangle=20√3 cm².

to find :

side of equilateral triangle

formulae :

area of an equilateral triangle(A)=(√3/4)a²

here, a=length of sides

solution :

$area \: of \: an \: equilateral \: triangle = (\frac{ \sqrt{3} }{4} ) {a}^{2} \\ \\ \implies20 \sqrt{3 } = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ \implies20 \cancel{ \sqrt{3} } = \frac{ \cancel{ \sqrt{3} }}{4} {a}^{2} \\ \\ \implies \: {a}^{2} = 80 \\ \\ \implies \: a = \sqrt{80} \\ \\ \implies \: a = 4 \sqrt{5} \: cm \\ \\ \\ \\ \underline{\boxed{\sf{ length \: of \: side \: of \: given \: equilatreal \: triangle = 4 \sqrt{5 \: cm} }}}$

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Answer 2

$\underline{\bold{Question:}}$

$\sf{Find\: the\: side \:of \:an \:equilateral\: triangle \:whose}$$\sf{area\: is \:20\sqrt{3}cm²}$

$\underline{\bold{Solution:}}$

$\bold{\red{➾\:Area = \dfrac{1}{2}×base×height}}$

$\bold{➾\:20\sqrt{3} = \dfrac{1}{2}×a×\sqrt{a²-\dfrac{a²}{4}}}$

$\bold{➾\:40\cancel{\sqrt{3}} =a×\dfrac{\cancel{\sqrt{3}}a}{2}}$

$\bold{➾\:80 =a²}$

$\bold{➾\:a = 4\sqrt{5}cm}$