Question 862757: David has 280 yards of fencing to enclose a rectangular area. Find the demensions of the rectangle that maximize the enclosed area.What is the maximum area?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! David has 280 yards of fencing to enclose a rectangular area. Find the demensions of the rectangle that maximize the enclosed area.What is the maximum area?
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let x=width
let y=length
2x+2y=280
x+y=140
y=140-x)
..
Area=xy=x(140-x)=140x-x^2
=-x^2+140x
complete the square:
=-(x^2-140x+4900)+4900
=-(x-70)^2+4900
This is an equation of a parabola that opens down with vertex at (70,4900)
maximum area=4900 sq yds
dimensions: 70 by 70 yds, a square.
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