Question

If the area of an equilateral triangel is
$81 \sqrt{3}$
cm² find its perimeter

Answer 1

$\mathsf{ Solution : } \\ \\ \mathsf{ We \: know \: that, } \\ \\ \mathsf{ \implies Area \:of \: equilateral \: \triangle = \: \dfrac{\sqrt{3}}{4} {a}^{2} } \\ \\ \mathsf{ \implies 81 \sqrt{3} \: {cm}^{2} \: = \: \dfrac{ \sqrt{3} }{4} {a}^{2} } \\ \\ \mathsf{ \implies {a}^{2} \: = \: \dfrac{ 81 \sqrt{3} \: {cm}^{2} \: \times \: 4 \: }{ \sqrt{3} } } \\ \\ \mathsf{ \implies {a}^{2} \: = \: 9 \: \times \: 9 \: \times \: 2 \: \times \: 2 \: {cm}^{2} } \\ \\ \mathsf{ \implies a \: = \: \sqrt{ \: {9}^{2} \: \times \: {2}^{2} \: {cm}^{2} } } \\ \\ \mathsf{ \implies a \: = \: 9 \: \times \: 2 \: {cm}} \\ \\ \mathsf{ \therefore \: a \: = \: 18 \: cm} \\ \\ \mathsf{ Now, } \\ \\ \mathsf{ \implies Perimeter \: of \: a n\: equilateral \: \triangle \: = \: 3a } \\ \\ \mathsf{ \qquad \qquad \qquad \: \: \qquad \qquad\qquad \qquad = \: 3 \: × \: 18 \: cm } \\ \\ \mathsf {\qquad \qquad \qquad \qquad \qquad \: \: \qquad \qquad = \: 54 \: cm }$


$\boxed{\mathsf{Hope \: it \: helps \: !! }}$