Question

A wire, when bent in the form of a square, encloses an area of 484 cm2. Find :

(i) one side of the square

(ii) length of the wire

(iii) the largest area enclosed, if the same wire is bent to form a circle.

Answer 1

(i)Area of Squre$=484c{m}^2$

$\therefore$ Side of Squre $=\sqrt{Area}$

$=\sqrt{484}=22cm$

(ii) $\therefore$ Perimeter, i.e. length of wire

$=4\times 22$

=88 cm

(iii) $\therefore$ Circumference of circle =88 cm

$2\pi r=88$

$2\times \frac{22}{7}\times r=88$

$r=\frac{88\times 7}{2\times 22}$

r =14 cm

$\therefore$ The largest are enclosed $=\pi r^2$

$=\frac{22}{7}\times 14\times 14$

$=616c{m}^2$

Hence (i)22 cm (ii)88 cm (iii)616 $c{m}^2$