Question

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. ...?

Answer 1

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