A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 180,000 square meters in order to provide enough grass for the herd. What dimensions would require the least amount of fencing if no fencing is needed along the river?

Answer: The dimensions are length 600metres and breadth = 300 metres

Explanation:

Area of rectangle = l * b

L b = 180,000

b = 180,000/L ... equation 1

Perimeter of rectangle = 2L + b

P = 2 (180,000) / L + L

P = 360,000/L + L

dp/dL = - 360,000/L^2 + 1

L^2 = 360,000

L = Squareroot of 360,000

L=600m

b = 180,000/600

b = 300m