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Question

# If the area of an equilateral triangle is $16\sqrt{3}{\mathrm{cm}}^{2}$, then its perimeter is (a) 48 cm (b) 24 cm (c) 12 cm (d) 36 cm

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Solution

## Given: The area of an equilateral triangle is $16\sqrt{3}{\mathrm{cm}}^{2}$. Let the length of the side of an equilateral triangle be x cm. $\mathrm{Area}\mathrm{of}\mathrm{an}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}×{x}^{2}\phantom{\rule{0ex}{0ex}}⇒16\sqrt{3}=\frac{\sqrt{3}}{4}{\left(x\right)}^{2}\phantom{\rule{0ex}{0ex}}⇒\frac{16\sqrt{3}×4}{\sqrt{3}}={\left(x\right)}^{2}\phantom{\rule{0ex}{0ex}}⇒{x}^{2}=64\phantom{\rule{0ex}{0ex}}⇒x=8\mathrm{cm}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{Perimeter}\mathrm{of}\mathrm{triangle}=3x\phantom{\rule{0ex}{0ex}}=3\left(8\right)\phantom{\rule{0ex}{0ex}}=24\mathrm{cm}$ Hence, the correct option is (b).

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