2012 · Q55
A square, a circle and an equilateral triangle have same perimeter. Consider the following statements:
- 1The area of square is greater than the area of the triangle.
- 2The area of circle is less than the area of triangle.
Which of the statements is/are correct?
Elementary MathematicsMensuration
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
For perimeter P the areas are P^2/16 (square), P^2/(4*pi) (circle), sqrt(3)*P^2/36 (triangle); the circle is largest and the triangle smallest.