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.

## Answer this Question

## Related Questions

- Math - A rectangular dog pen is to be constructed using a barn wall as one side ...
- algebra - Ian wants to build a rectangular pen for his animals. One side of the ...
- math - a rectangular pen is to be constructed alongside a barn using 120 feet of...
- Geometry - A farmer wants to fence in a rectangular pen using the wall of a barn...
- Math - Manuel wants to build a rectangular pen for his animals. One side of the ...
- math - Farmer Hodges has 50 feet of fencing to make a rectangular hog pen ...
- math - a rectangular garden with an area of 2112 square feet is to be located ...
- math - A farmer will make a rectangular pen with 100 feet of fence using pasrt ...
- calculus optimization problem - A farmer has 460 feet of fencing with which to ...
- Math Calculus - Three sides of a fence and an existing wall form a rectangular ...