SOLUTION: A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?

Algebra ->  Length-and-distance -> SOLUTION: A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?       Log On


   

Question 281331: A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's a square.
750 on a side --> 562500 sq feet
---------------
Do you need proof it's a square, or will you trust me?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?
----------------------
Perimeter = 2(L+W)
3000 = 2(L+W)
1500 = L+W
L = W-1500
---------------------
Area = W*L
A = W(W-1500)
A = W^2-1500W
---
Quadratic equation with a = 1, b = -1500
--------------------------------------------
Maximum occurs when W = -b/2a = 1500/2 = 750 ft.
---
Since L+W = 1500
L = 1500-750
L = 750ft
======
Final Answer: length and width need both be 750'
===================================================
Cheers,
Stan H.