Question

4. The circumference of a circle is the same as the perimeter of a square. The circle has a radius of
28 cm. Find the side of the square.
​

Answer 1

SOLUTION

GIVEN

The circumference of a circle is the same as the perimeter of a square. The circle has a radius of

28 cm.

TO DETERMINE

The side of the square.

EVALUATION

Here it is given that the circumference of a circle is the same as the perimeter of a square. The circle has a radius of 28 cm.

Radius of the circle = 28 cm

∴ Circumference of the circle

$\sf{ = 2\pi \times 28 \: \: \: cm}$

Let side of the square = a cm

∴ Perimeter of the square = 4a cm

So by the given condition

$\sf{4a = 2\pi \times 28}$

$\displaystyle \: \sf{ \implies \: 4a = 2 \times \frac{22}{7} \times 28}$

$\displaystyle \: \sf{ \implies \: 4a = 8 \times 22}$

$\displaystyle \: \sf{ \implies \: a = 2 \times 22}$

$\displaystyle \: \sf{ \implies \: a = 44}$

Hence the side of the square = 44 cm

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