SOLUTION: Can you give me detailed steps on how to set up and solve? Scott wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can you give me detailed steps on how to set up and solve? Scott wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three      Log On


   

Question 945343: Can you give me detailed steps on how to set up and solve?

Scott wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Scott has 650 feet of fencing, what dimensions would maximize the area of the pen?
a) Let w be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of w
Area =
b) What width w would maximize the area?
w =

Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
A square shape will maximize the area of a rectangle. Cut the fencing into three equal parts. One more part of equal size will be the barn, not needing the available fence material.


MORE DETAILS

A, for area
w, width
L, length
Assuming 1*L will be against the barn
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L%2B2w=650, the amount of fence material to form the rectangular enclosure;
A=wL, basic formula for area;


Use the fencing equation to find a formula for L.
L=650-2w

Substitute for L in the area equation.
highlight%28A=w%28650-2w%29%29 OR highlight%28A=-2w%5E2%2B650w%29
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Area A is a function of w. This is a parabolic, or quadratic function, and based on the
features of the equation, you know A has a maximum value...
Do the rest.