2016 · Q54
A circle and a square have the same perimeter. Which one of the following is correct ?
Elementary MathematicsMensuration
- ATheir areas are equal
- BThe area of the circle is larger
- CThe area of the square is π/2 times area of circle
- DThe area of the square is k times area of circle
Explanation
For a fixed perimeter, the circle encloses the greatest possible area — the isoperimetric inequality. So with equal perimeters, the circle's area is strictly larger than the square's. Hence option B.