Question

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}$ cm, then the area $\left(inc{m}^2\right)$ of the triangle is?

• A. $36\sqrt{2}$
• B. $36\sqrt{3}$
• C. $64\sqrt{2}$
• D. $64\sqrt{3}$

Answer 1

The correct option is D $64\sqrt{3}$

Diagonal of the square = $12\sqrt{2}=d$
Area of square $=\frac{1}{2}{d}^2$ = $\left(6\sqrt{2}\right)\left(12\sqrt{2}\right)$ = $144$ $c{m}^2$
Side of square $=\sqrt{Area}=12$ cm
Perimeter of square $=$ Perimeter of Triangle $=12\times 4=48$ cm
Length of the triangle $=\frac{48}{3}=16$ cm
Area of triangle $=\frac{\sqrt{3}}{4}{16}^2=64\sqrt{3}$ $c{m}^2$