SOLUTION: if mr smith has 80 ft of fence to close his garden in with would he get more square ft out of a rectangle or a square? Why

Question 171385: if mr smith has 80 ft of fence to close his garden in with would he get more square ft out of a rectangle or a square? Why
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
if mr smith has 80 ft of fence to close his garden in with would he get more square ft out of a rectangle or a square? Why
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He would get the most from a circle. But the greatest area in a rectangular form is a square. I don't know what it meant by why. It's because it's the most area.
The sides of the square would be 20 feet, giving 400 square feet. Making them 19 by 21 gives 399 square feet.
Area = LW = L*(40-L)
Area = 40L - L^2
Set the 1st derivative to zero and solve for L to get the maximum:
40 - 2L = 0
2L = 40
L = 20
That's a proof, not really "why"
BTW, a square is a rectangle, a regular rectangle.

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