SOLUTION: sarah and beth receive 45 yards of fencing to use to enclose a playground for their center. if they use the side of the school as one edge of the playground, they will need to fenc

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Question 407463: sarah and beth receive 45 yards of fencing to use to enclose a playground for their center. if they use the side of the school as one edge of the playground, they will need to fence three sides. if they want to create a playground that will provide the greatest area for the children, find the dimensions of the playground.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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45 yards of fencing to use to enclose a playground for their center.
if they use the side of the school as one edge of the playground, they will need to fence three sides.
if they want to create a playground that will provide the greatest area for
the children, find the dimensions of the playground.
:
Perimeter for only 3 sides
L + 2W = 45
L = (45-2W)
:
Area
A = L * W
Replace L with (45-2W)
A = (45-2W)*W
A = -2W^2 + 45W
a quadratic equation, the axis of symmetry will be the max area
Find the Axis of symmetry: W = -b/(2a) in this equation: a=-2; b=45
w =%28-45%29%2F%282%2A-2%29
w = %28-45%29%2F%28-4%29
w = +11.25 yds is the width for max area
then
45 - 2(11.25) = 22.5 yds is the length
:
Max area: 22.5 * 11.25 = 253.125 sq/yds