Question

The perimeter of a particular equilateral triangle is numerically equal to the area of the triangle. Find the perimeter of the triangle.

• A. $3$
• B. $4$
• C. $4\sqrt{3}$
• D. $12\sqrt{3}$
• E. $18\sqrt{3}$

Answer 1

The correct option is D $12\sqrt{3}$

The area(A) of an equilateral triangle. If the length of each side of the triangle is $a$,
$A=\frac{\sqrt{3}}{4}{a}^2$
The perimeter(P) of an equilateral triangle. If the length of each side of the triangle is $a$, $P=3a$
Since, we have the perimeter equals the area for this triangle,
$\Rightarrow 3a$$=\frac{\sqrt{3}}{4}{a}^2$
$\Rightarrow 12a=\sqrt{3}{a}^2$
$\Rightarrow 12=\sqrt{3}a$
$\Rightarrow a=4\sqrt{3}$
The perimeter(P) of an equilateral triangle $=3a=3\times 4\sqrt{3}=12\sqrt{3}$
Hence, option D is correct.