SOLUTION: Al Yazia has 24 meter of fence. she want to make the largest rectangular area possible for her rabbit to play in. What length should make each side of the rabbit pen? (Show all you

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Question 541836: Al Yazia has 24 meter of fence. she want to make the largest rectangular area possible for her rabbit to play in. What length should make each side of the rabbit pen? (Show all your work and explain how you find the largest area.
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Answer by Alan3354(69443) About Me  (Show Source):
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Al Yazia has 24 meter of fence. she want to make the largest rectangular area possible for her rabbit to play in. What length should make each side of the rabbit pen? (Show all your work and explain how you find the largest area.
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It's a square, 6 meters on a side = 36 sq meters.
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Perimeter = 2L + 2W = 24
L + W = 12
W = 12 - L
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Area = L*W = L*(12 - L)
Area+=+12L+-+L%5E2
-L%5E2+%2B+12L+-+Area+=+0
The coefficient of the L^2 is negative, so it's a maximum.
Find the vertex of the parabola
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Line of Symmetry = -b/2a = -12/-2
L = 6
The vertex is on the LOS, so L = 6 is the maximum.
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6*6 = 36
5*7 = 35
4*8 = 32
Any other combination is less than 36.