Dimensions of a Rectangle

Question

A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 36 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.

Answer 1

In order to maximize the area of any polygon, the side lengths need to be the same. Why?

A rectangle 15 km by 3 km has a perimeter of 36 but an area of 45 km^2

However a rectangle that is 10 km by 8 km has a perimeter of 36 but an area of 80 km^2.

So find the rectangle with four equal sides. (We commonly refer to it as a square!) Then use the lengths for a square with a perimeter of 36.