Question

7) A rectangular pen can be constructed using the side of a barn as one boundary and 5500 ft. of fence to make the other three sides. Find the length and width of the rectangle to make the largest area.
Hint: Draw a picture- and label the sides of the rectangle. And solve the problem.

Answer 1

let each of the two equal sides be x
let the single side by y
then y+2x = 5500
y = 5500 - 2x

area = xy
= x(5500-2x)
= -2x^2 + 5500

Since you labeled it "college" math, I will assume you know Calculus

d(area)/dx = -4x + 5500
= 0 for a max of area
4x = 5500
x = 1375
y = 5500-2(1375) = 2750

the pen is 1375 ft by 2750 ft, with the side of 2750 parallel to the barn.