Question

A square and an equilateral triangle have the same perimeter. If the diagonal of the square is $12\sqrt{2}cm$, then the area of the triangle is

• A. $24\sqrt{3}c{m}^2$
• B. $24\sqrt{2}c{m}^2$
• C. $64\sqrt{3}c{m}^2$
• D. $32\sqrt{3}c{m}^2$

Answer 1

Answer: (C)

$64\sqrt{3}c{m}^2$

Let $a$ be the side of square.

Diagonal of the square is $=12\sqrt{2}cm$

$a\sqrt{2}=12\sqrt{2}cm$

$a=12cm$

Perimeter of Square $=4a=4\times 12=48cm$

Side of equilateral triangle $=\frac{48}{3}=16cm$

Area $=\frac{\sqrt{3}}{4}\times 16cm\times 16cm$

$=64\sqrt{3}c{m}^2$