Question

A square and an equilateral triangle have equal perimeters, if the diagonal of the area of the plot is

• A. $24\sqrt{2}$
• B. $24\sqrt{3}$
• C. $48\sqrt{3}$
• D. $64\sqrt{3}$

Answer 1

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

Side of the square $=\frac{1}{\sqrt{2}}\times 2\sqrt{2}=12$
Perimeter of the equilateral triangle
$=4\times 12=48$
Side of this triangle $=48÷3=16$
Area of this triangle $=\frac{\sqrt{3}}{4}\times {\left(16\right)}^2=64\sqrt{3}$