Question

Suppose two rectangles both have a perimeter of 40 m. Must they also have the same area? Try several examples to test your conjecture.

Answer 1

No, for a fixed perimeter for a rectangle, a square maximizes area. So the area of 100 square units or a square of side 10 would yield the largest area. Draw it.

Take another rectangle that is not a square. Suppose its dimentions are 2 units by 18 units. The perimeter is still 40 units but the area is 36 square units, much less than that of the square with the same perimeter.

However, there are occasions when a rectangle such as the 2 by 18 would be desirable as in the case of a pen for a dog to run.