Posted by **Chelsea** on Tuesday, January 31, 2012 at 7:22pm.

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)

- Math -
**Reiny**, Tuesday, January 31, 2012 at 8:15pm
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

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