Question 869244: the perimeter of a rectangle is 56 yards. what are the dimensions of the rectangle with maximum area?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! the perimeter of a rectangle is 56 yards. what are the dimensions of the rectangle with maximum area?
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let x=length
let y=width
2x+2y=56
x+y=28
y=28-x
Area=xy=x(28-x)=28x-x^2
Area=-x^2+28x
complete the square:
Area=-(x^2-28x+196)+196
=-(x-14)^2+196
This is an equation of a parabola that opens downward with vertex at (14,196), which means maximum area of 196 occurs when x, the length=14)
dimensions of the rectangle with maximum area? 14 yds by 14 yds, a square.
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