Question

The area of a square plot is $6084m^2$. Find the length of the wire which can go four times along the boundary of the plot.

Answer 1

Area of the square plot $=6084m^2$
Area of square plot $=(Side{)}^2$
$(Side{)}^2=6084$

$\begin{array}{cc}2& 6084\\ 2& 3042\\ 3& 1521\\ 3& 507\\ 13& 169\\ 13& 13\\ & 1\end{array}$

$6084=2\times 2\times 3\times 3\times 13\times 13$

$\therefore side=\sqrt{6084}m=\sqrt{2\times 2\times 3\times 3\times 13\times 13}=2\times 3\times 13=78m$
$\therefore$ Perimeter of the square plot $=4\times side=(4\times 78)m=312m$
$312m$ wire is needed to go along the boundary of the square plot once.
The required length of the wire that can go four times along the boundary

$=4\times$ Perimeter of the square plot
$=(4\times 312)m=1248m$