SOLUTION: please help me on this one....A farmer has 60m of fencing to make a rectangular pen for his goat, find the maximum possible area of the pen.... i tried to derive the expression : l

Algebra ->  Formulas -> SOLUTION: please help me on this one....A farmer has 60m of fencing to make a rectangular pen for his goat, find the maximum possible area of the pen.... i tried to derive the expression : l      Log On


   

Question 988965: please help me on this one....A farmer has 60m of fencing to make a rectangular pen for his goat, find the maximum possible area of the pen.... i tried to derive the expression : l=30-w. And the expression for the area in terms of the width : A=-w^2 +30w
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
length L
width w
A for AREA
perimeter is 60 feet, equal to the amount of fencing.
2w%2B2L=60
w%2BL=30

A=wL
A=w%2830-w%29
A=30w-w%5E2
A=-w%5E2%2B30w------Just as you have.

Your question is, what is w and L for maximum area A ?

w and L must be each greater than 0.
A is a parabola function and A=-w%5E2%2B30w has a maximum point for its vertex; and A has two x-axis intercepts. The maximum value for A occurs in the exact middle of the roots. w is really the HORIZONTAL number line and A is for the vertical number line.

Roots for A?
-w%5E2%2B30w=0
Solve for w, and find what is the value in the middle?
Now, what is A at that middle value of w?