Question

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $6\sqrt{2}$ cm, then the area of the triangle is

• A. $16\sqrt{2}$ cm${}^2$
• B. $16\sqrt{3}$ cm${}^2$
• C. $12\sqrt{2}$ cm${}^2$
• D. $12\sqrt{3}$ cm${}^2$

Answer 1

Answer: (B)

$16\sqrt{3}$ cm${}^2$

Let the side of equilateral triangle be "a" and that of square be "x", then
$\Rightarrow 3a=4s$
We are given,
Length of the diagonal $=\sqrt{2}\times s=6\sqrt{2}cm$
$\Rightarrow s=6cm$
$\Rightarrow a=8cm$
Area of equilateral triangle $=\frac{\sqrt{3}}{4}\times a^2$
$A=16\sqrt{3}c{m}^2$