Question

A square and a circle both have a perimeter of $88cm.$ Which one has more area$?$

Answer 1

Perimeter of square $=4a$

It is given that perimeter of square $=88cm$

$4a$$=88cm$

$a=22cm$

Perimeter of circle $=2\mathrm{\pi r}$

It is given that perimeter of circle $=88cm$

$2\mathrm{\pi r}$$=88$

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

$r=\frac{88\times 7}{44}$

$r=2\times 7$

$r=14cm$

Area of circle$=\mathrm{\pi }{\mathrm{r}}^2$

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

$=22\times 2\times 14$

$=616c{m}^2$

Area of square $=22\times 22$

$=484c{m}^2$

Hence the area of circle is larger