Question

The perimeter of an equilateral triangle is equal to that of a square.If the area of the triangle is $16\sqrt{3}{cm}^2$ . what is the area of the square (in sq cm)?

• A. $18\sqrt{3}$
• B. $18$
• C. $36$
• D. $36\sqrt{3}$

Answer 1

The correct option is C $36$

Let the side of equilateral triangle be $a$.and the square be $s$.

So, $3a=4s$

Area of triangle$=\frac{\sqrt{3}}{4}{a}^2=16\sqrt{3}$

$⟹a=8$

$s=\frac{3}{4a}=\frac{3\times 8}{4}=3\times 2=6$

Area of square$=s^2=6^2=36$.