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(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.

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