SOLUTION: 4.) Find the maximum possible area of a rectangle with a perimeter of 100 feet. I've drawn a picture, labeled both the length and width on the rectangle, and written down the fo

Question 213298: 4.) Find the maximum possible area of a rectangle with a perimeter of 100 feet.
I've drawn a picture, labeled both the length and width on the rectangle, and written down the formulas for perimeter and area.
But now... I'm stuck. If you could explain how to finish this problem.. I would be grateful! Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the maximum possible area of a rectangle with a perimeter of 100 feet.
I've drawn a picture, labeled both the length and width on the rectangle, and written down the formulas for perimeter and area.
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Perimeter = 2(L + W)
100 = 2(L+W)
L+W = 50
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Let width be W
Then length = 50-W
--------
Area = length * width
A = (50-W)W
A = 50W-W^2
--
This is a quadratic with a = -1, b = 50:
Maximum area occurs when W = -b/2a = -50/-2 = 25
Since W = 25 and L+W=50, L = 25
----------------
Maximum area is 25*25 = 625 sq. units
=========================================
Cheers,
Stan H.
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