Question

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

• A. $372\cdot 58$ sq. m
• B. $337\cdot 17$ sq. m
• C. $462\cdot 13$ sq. m
• D. $274\cdot 13$ sq. m

Answer 1

Answer: (A)

$372\cdot 58$ sq. m

Given,A wire when bent in the form of a square encloses an area of 484 sq. m .
Area of Square$={\left(side\right)}^2$
or, 484 $={\left(side\right)}^2$
or, side $=\sqrt{484}=22cm$
Perimeter of square$=$ 4 $\times$ side
$=$ 4 $\times$ 22
$=$ 88 cm.
When same wire is formed into equilateral triangle,then perimeter of square is equals to perimeter of triangle.
$\therefore$ Perimeter of equilateral triangle$=$ 88 cm
or, 3$\times$ side $=$ 88 cm
or, side $=$ $\frac{88}{3}$cm.
Area of equilateral triangle thus formed $=\frac{\sqrt{3}\times {\left(side\right)}^2}{4}$
$=\frac{\sqrt{3}\times {\left(\frac{88}{3}\right)}^2}{4}$
$=372.58{cm}^2$