Question

The area of an equilateral triangle is 40013 m²
its perimeter is
a) 120 m b) 150 m c) 90 m d) 135 m​

Answer 1

${\bold {\huge {\text {\underline{Question :- }}}}}$

• The area of an equilateral triangle is 400√3 m². Its perimeter is ______.

${\bold {\large {\text {\underline{Options :- }}}}}$

(a) 120 m (b) 150 m (c) 90 m (d) 135 m

${\bold {\huge {\textsf {\underline{Solution :- }}}}}$

We know,

$\large \bf Area \: \: of \: \: equilateral \: \: triangle \\ \\ \sf \rightarrow \: \: \: \: \: \frac{ \sqrt{3} }{4} {a}^{2} = 400 \sqrt{3} \\ \\ \sf \rightarrow \: \: \: \: \: \: \: \: \: \: \: \: {a}^{2} = \frac{400 ( \cancel{\sqrt{3}}) \times 4 }{ \cancel{ \sqrt{3}} } \\ \\ \sf \rightarrow \: \: \: \: \: \: \: \: \: \: \: \: {a}^{2} = 1600 \\ \sf \rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: a = \sqrt{1600} = 40 \: m$

Therefore,

$\large \text{Perimeter of this triangle} \\ \\ \bf = > \: \: \: 3 \times side \\ \bf = > \: \: \: (3 \times 40) \: m \\ \bf = > \: \: \: \red{120 \: m}$

• Hence, Option (a) is the correct answer.

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