Problem: A circle and a square have the same perimeter. Then:
Answer Choices:
A. their areas are equal
B. the area of the circle is the greater
C. the area of the square is the greater
D. the area of the circle is times the area of the square
E. none of these
Solution:
For a given perimeter the circle has the largest area;
let be the common perimeter, and the areas of the circle and the square, respectively. Then
Since .