SOLUTION: 48. A rancher has 200 feet of fencing to build a rectangular corral alongside an existing fence. Determine the dimensions of the corral that will maximize the enclosed area.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 48. A rancher has 200 feet of fencing to build a rectangular corral alongside an existing fence. Determine the dimensions of the corral that will maximize the enclosed area.      Log On


   

Question 53386This question is from textbook Applied College Algebra
: 48. A rancher has 200 feet of fencing to build a rectangular corral alongside an existing fence. Determine the dimensions of the corral that will maximize the enclosed area. This question is from textbook Applied College Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A rancher has 200 feet of fencing to build a rectangular corral alongside an existing fence. Determine the dimensions of the corral that will maximize the enclosed area.
--------------
Draw the picture.
Two of the corral sides are of equal length; let that common length be "x".
The third side has length "200-2x".
The area of the corral is x(200-2x)=200x-2x^2
EQUATION:
Area = -2x^2+200x
This is a quadratic with a=-2, b=200
The maximum is at x=-b/2a = -200/-4=50ft.
Then 200-2x=100 ft
So the corral is 50 ft by 100 ft
Cheers,
Stan H.