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

The correct option is C $64\sqrt{3}c{m}^2$

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

Side of square$a=\frac{d}{\sqrt{2}}=\frac{12\sqrt{2}}{\sqrt{2}}=12cm$

Perimeter of square$=40=4\times 12=48cm$

Also, perimeter of square=Perimeter of equilateral triangle of each side $b$

$48=3b$

$\Rightarrow b=16cm$

$\therefore$Area of equilateral $△=\frac{\sqrt{3}}{4}\times b^2=\frac{\sqrt{3}}{4}\times 16\times 16=64\sqrt{3}c{m}^2$