Some cowboys plan to build a rectangular corral in a canyon. They have 500 feet of fencing to use for three sides of the rectangle (the canyon wall is used for the 4th side).

Question

a) What is the maximum area that they can fence in?
b) What are the dimensions of the rectangle?

Answer 1

let the side parallel to the canyon wall be y ft
let each of the other two shorter and equal sides be x

2x + y = 500
y = 500-2x

area = xy
= x(500-2x)
= 500x - 2x^2

since you labeled it Calculus
d(area)/dx = 500 - 4x
= 0 for a max of area
4x = 500
x = 125

when x = 125 , y = 500 - 2(125) = 250
max area = xy = 125(250) = 31250 ft^2 when the longer side is 250 ft and the two shorter sides are 125 ft each

Answer 2

Some cowboys plan to build a rectangular corral in a canyon. They have 200 feet of fencing to use for three sides of the rectangle (the canyon wall is used for the 4th side).
a) What is the maximum area that they can fence in?
b) What are the dimensions of the rectangle?

Answer 3

My bad.