A Rancher wants to enclose 2 rectangular area near a river, one for sheep and one for cattle. There is 240 yd. of fencing available. What is the largest total area that can be enclosed ...?

Assuming the rectangles made will be of the same size:

Perimeter = 2 (l + b)

For two rectangles,

Perimeter = 2 x 2 (l + b)

240 = 4 (l + b)

l + b = 60

l = 60 - b

Area = l x b

Area = 60b - b²

dA/db = 60 - 2b

Putting dA/db = 0

b = 30

Length = 60 - 30 = 30

Greatest available area of one triangle = 30 x 30

= 900 sq yd

Greatest total area that can be enclosed in both triangels

= 900 x 2

= 1800 sq yd