Question

Oliver’s company needs to enclose a rectangular area of 5200 square feet on three sides with barbed wire fencing. Find the dimensions of that will minimize the amount of fencing required (thus minimizing building cost). Hint: minimizing the amount of fencing is equivalent to minimizing the perimeter, or distance around, the three sides of the enclosure.

Answer 1

Area of the garden = 5200 m2
⇒ l × b = 5200
⇒ l = 5200/b
Garden is fenced on three sides.
Length of fencing = 2b + l
⇒ 2*(5200/l) + l, differentialting it to minimize,
⇒ -10400 / l^2 + 1 = 0,

l = sqrT( 10400) = 101.9804 ft

So, and b = 5200/101.9804 = 50.9902 ft

So, the dimensions of that will minimize the amount of fencing are l = 101.9804 ft , b= 50.9902 ft