ABC26GN4480 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the area of an equilateral triangle is $24 \sqrt{3} \mathrm{sq} . \mathrm{cm}$, then its perimeter is
(a)$2 \sqrt{6} \mathrm{cm}$
(b)$4 \sqrt{6} \mathrm{cm}$
(c)$12 \sqrt{6} \mathrm{cm}$
(d)96 cm
Answer
Explanation
Area of an equilateral triangle of side $a \mathrm{cm}=\left(\frac{\sqrt{3}}{4} a^{2}\right) \mathrm{cm}^{2}$. $$\begin{aligned} & \therefore \frac{\sqrt{3}}{4} a^{2}=24 \sqrt{3} \Leftrightarrow a^{2}=96 \Leftrightarrow a=4 \sqrt{6} \mathrm{cm} . \\ & \therefore \text { Perimeter }=3 a=1212 \sqrt{6} \mathrm{cm} . \end{aligned}$$
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