Question

A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can be enclosed? (Note: The side along the barn will not require fencing)

Answer 1

let the width of the field be x ft
let the length be y ft
so y + 2x = 80
or y = -2x + 80

area = xy
= x(-2x+80)
= -2x^2 + 80x

do you know Calculus?
if so ...
d(area)/dx = -4x + 80 = 0 for a max area
4x = 80
x = 20
width is 20 ft, length is 40 ft.
largest area = 20(40) = 800 ft^2

If you don't know Calculus, complete the square