A cattle pen: A rancher wants to use a fence as an enclosure for a rectangular cattle pen with area 400 square feet. a. Suppose he decides to make one side of the pen 40 feet long. Draw a picture and...

A cattle pen: A rancher wants to use a fence as an enclosure for a rectangular cattle pen with area 400 square feet.

a. Suppose he decides to make one side of the pen 40 feet long. Draw a picture and label the length of each side of the pen. What is the length of each side? What is the total amount of fence needed?

b. What would be the total amount of fence needed if the pen were a square?

c. Can two rectangles with the same area have different perimeters?

d. Find a formula for a function F = F (l) that gives total amount of fence, in feet, required in terms of the length l, in feet, of one of its sides. (Hint: First draw a picture of the pen and label one side l. Next figure out the lengths of the other sides in terms of l.)