Question
Find the perimeter of an equilateral triangle whose area is $16 \sqrt{3} \ cm$.
✓
Answer
We know that, Area of an equilateral triangle $(A)$ of side $a$ is
$A=\frac{\sqrt{3}}{4} a ^2$
Here, $A=16 \sqrt{3}$
$\Rightarrow 16 \sqrt{3}=\frac{\sqrt{3}}{4} a ^2$
$\Rightarrow 16=\frac{ a ^2}{4}$
$\Rightarrow 4 \times 16= a ^2$
$\Rightarrow a$
$=2 \times 4$
$=8$
i.e. side of the equilateral triangle is $8 \ cm$
The perimeter of an equilateral triangle of side $a=3 a$
$\Rightarrow$ The Perimeter of an equilateral triangle of side $8 \ cm$
$=3 \times 8$
$=24 \ cm \text {. }$
$A=\frac{\sqrt{3}}{4} a ^2$
Here, $A=16 \sqrt{3}$
$\Rightarrow 16 \sqrt{3}=\frac{\sqrt{3}}{4} a ^2$
$\Rightarrow 16=\frac{ a ^2}{4}$
$\Rightarrow 4 \times 16= a ^2$
$\Rightarrow a$
$=2 \times 4$
$=8$
i.e. side of the equilateral triangle is $8 \ cm$
The perimeter of an equilateral triangle of side $a=3 a$
$\Rightarrow$ The Perimeter of an equilateral triangle of side $8 \ cm$
$=3 \times 8$
$=24 \ cm \text {. }$
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