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what is the largest are of rectangular area that can be enclosed in sixteen meter fence
?

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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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