The area of an equilateral triangle is

Question:

The area of an equilateral triangle is $36 \sqrt{3} \mathrm{~cm}^{2}$. Its perimeter is

(a) 36 cm

(b) $12 \sqrt{3} \mathrm{~cm}$

(c) 24 cm
(d) 30
 cm

 

Solution:

(a) 36 cm

Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$

$\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=36 \sqrt{3}$

$\Rightarrow(\text { Side })^{2}=144$

$\Rightarrow$ Side $=12 \mathrm{~cm}$

Now,
Perimeter = 3 × Side = 3 × 12 = 36 cm

 

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