Question

The area of an equilateral triangle is 2 √3cm^2. Find its side.

Answer 1

$\large\bf\underline \orange{Given:-}$

• Area of equilateral triangle = 2√3cm²

$\large\bf\underline \orange{To \: find:-}$

• Side of triangle.

$\huge\bf\underline \green{Solution:-}$

$\rm \: area \: of \: equilateral \triangle = \bf \frac{ \sqrt{3} }{4} \times (side) {}^{2}$

• Let the side be x cm

$: \implies \rm\: \frac{ \sqrt{3} }{4} \times \: x {}^{2} = 2 \sqrt{3} \: \\ \\ : \implies \sf\: {x}^{2} = 2 \cancel{\sqrt{3}} \times \frac{4}{ \cancel{\sqrt{3}} } \\ \\ : \implies \sf\: {x}^{2} = 2 \times 4 \\ \\ : \implies \sf\: {x}^{2} = 8 \\ \\ : \implies \sf\:x = \sqrt{8} \\ \\ : \implies {\boxed {\bf {x = 2 \sqrt{2} }}}$

Hence,

side of equilateral triangle = 2√2 cm

Answer 2

✯✯ QUESTION ✯✯

The area of an equilateral triangle is 2 √3cm^2. Find its side..

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✰✰ ANSWER ✰✰

• Let the side of Equilateral Triangle be = y cm.
• Given Area of Equilateral Triangle = 2√3cm²..

➙Now ,

✔Area of Equilateral Triangle = √3/4 × (Side)²

➜Putting Values : -

$\longmapsto\tt{2\sqrt{3}=\dfrac{\sqrt{3}}{4}\times{{y}^{2}}}$

$\longmapsto\tt{2\sqrt{\cancel{3}}\times\dfrac{4}{\sqrt{\cancel{3}}}={y}^{2}}$

$\longmapsto\tt{4\times{2}={y}^{2}}$

$\longmapsto\tt{8={y}^{2}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{y}\orange{=}\purple{2\sqrt{2}}}}$

➥So,Side of Equilateral Triangle is 2√2 cm...

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