Question

A square field having area $196{\text{cm}}^2$ is to be fenced with wire. What length of the wire would be saved if the field were circular with radius 7 cm?

• A. 6 cm
• B. 12 cm
• C. 14 cm
• D. 44 cm

Answer 1

The correct option is B 12 cm

Area of a square = ${\text{side}}^2$
Area of the field =196 cm${}^2$=
Hence the side of the square = 14 cm ( square root of 14)
Perimeter of the square = 4s = 4 $\times$ 14 = 56 cm
If the field were circular and had a radius of 7 cm, then it would have a circumference of $2\times \frac{22}{7}\times 7$ units.
i.e., Circumference of the field = 44 units
$⟹$ Amount of wire that would have been saved = 56 - 44 = 12 cm