Question

What is the length of the side of a square that has area smaller than the area of a circle with radius r cm. Answer: The length of the side of the square is less than cm

Answer 1

Therefore the length of side of a square is less than
`√(\pi) r` cm.

Explanation:

Square:

• The area of a square = side²
• The perimeter of a square = 4× side

Circle:

• The area of a circle is π r²
• The perimeter of a circle 2πr.

Consider the length of side of the square be l.

The area of the square is = l² square units

The area the circle is = π r²

Given that the area of the square is smaller than the area of circle.

l²< π r²

Square root on both sides of inequality

`√(l^2) <√(\pi r^2)`

`\Rightarrow l<√(\pi) r`

Therefore the length of side of a square is less than
`√(\pi) r` cm.