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Find the side of an equialateral triangle if it's area is 9√3 cm2​

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Step-by-step explanation:

We know that the area of an equilateral triangle of side a cm is

  • [tex] \rm \: Equilateral \: Triangle = \cfrac{ \sqrt{3} }{4} {a}^{2} \: cm[/tex]

Let a cm here be 9√3 then we could get our solution.

[tex] \rm\implies \rm 9 \sqrt{3} = \cfrac{ \sqrt{3} }{4} \: a {}^{2} [/tex]

[tex] \implies \rm \: \cfrac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3} [/tex]

[tex] \implies \rm \: a {}^{2} = 36[/tex]

[tex] \implies \rm \: a = \sqrt{36} = \sqrt{6 \times 6} [/tex]

[tex] \implies \rm \: a = 6 \: cm[/tex]

Thus, the side of the equilateral triangle is 6 cm.

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