Can you help with my Precalculus?

Question

in my Precalculus homework, the question is “There has to be a rectangular area of 1680 ft sq. for my pig. There is the wall of a barn for one side. How much fencing would you need to buy?” Yes that’s all of the information given.

Im confused on how to approach this. Can you help?

Answer 1

off hand guess is 116 feet of fencing needed

side parallel to the barn wall should be twice the length of the sides perpendicular to the barn wall.

that makes it about 29 feet for 2 sides, and about 58 feet for the longer side, grand total about 116 feet

A=1680 ft^2 = xy

2x +y = fencing needed = f

f = 2x+y = 2x + 1680/x

take derivatives of f, set = 0, solve for x

f'(x) = 2 -1680/x^2 =0

2x^2 = 1680

x^2 = 840

x = sqr840 = about 28.99828 feet for each of the 2 perpendicular sides

y = 2x = the longer side= about 57.9655 ft

4x = fencing needed= 115.93101 feet total