Posted by aa on Monday, September 19, 2011 at 7:20am.
I am sure that I have answered this one recently
Let the width of the rectangle = w and the height = h
2w+2h=16 or
w=8-h
the area=wh or
area = (8-h)h = 8h-h^2 =a
there are a couple of ways to finding the maximum area. You could plot area against h and find where h is a maximum.
Alternatively the area is a maximum when da/dh=0
da/dh=8-2h, which is zero when h=4
i.e. the maximum area is when h=4 and w=4
so the largest area is 16 m^2
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