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 Square = 484 cm²
Side of Square = `sqrt("Area")` = `sqrt484` = 22 cm
(ii)

Perimeter, i.e. length of wire = 4 x 22 = 88 cm
(iii)

Circumference of circle = 88 cm
2πr = 88

`2 xx 22/7 xx r = 88`

`r = (88 xx 7)/(2 xx 22)`

r = 14 cm

∴ The largest area enclosed = `pir^2`

= `22/7 xx 14 xx 14`

= 616 cm²

Hence (i) 22 cm (ii) 88 cm (iii) 616 cm²