Question

A wire when bent in the form of a square encloses an area of $484m^2$. Find the largest area enclosed by the same wire when bent to form an equilateral triangle.

Answer 1

Given area of square $=484m^2$

$\Rightarrow a^2=484m^2$

$a=22m$

now perimeter of square $=4a=88m=$ perimeter triangle

$3a=88$

$a=\frac{88}{3}$

$=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times \frac{88}{3}\times \frac{88}{3}=\frac{\sqrt{3}}{9}\times 1936$