Posted by Michala on Sunday, July 20, 2014 at 1:38pm.
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.

College math  Reiny, Sunday, July 20, 2014 at 3:02pm
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(55002x)
= 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 = 55002(1375) = 2750
the pen is 1375 ft by 2750 ft, with the side of 2750 parallel to the barn.
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