Question

If the length of a rectangle with a constant area varies inversely with its width, how could you determine the greatest perimeter of the rectangle

Answer 1

there is no greatest perimeter.

The least perimeter is when the rectangle is a square.
Consider an area of 16
4x4 has p=16
2x8 has p=20
1x16 has p=34
1/2 x 32 has p=65
.01 x 1600 has p=3200.02