Question

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

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

Answer 1

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

Square and equilateral triangle have same perimeter

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

So side $=\frac{12\sqrt{2}}{\sqrt{2}}cm=12cm$

Perimeter $=12\times 4cm=48cm$

Triangle side $\frac{48}{3}cm16cm$

Area $=\frac{\sqrt{3}}{4}{16}^2=64\sqrt{3}sqcm$

Answer $D$