The maximum or minimum You have 84 ft of fencing to enclose

The maximum or minimum. You have 84 ft of fencing to enclose a rectangular plot that borders your house. If you do not fence the side along your house, find the length and width of the plot that will maximize the area. above the around t seconds after the object has been

Solution

Given that 84ft of fencing to enclose a rectangular plot that borders house.

Means perimater of house = 84ft.

Need to find the length and width of the the plot which maximize the area.

Let length of the plot = Lft

and width of the the plot = W ft

Perimeter = 84ft

2(L + W) = 84

L + W = 42

L = 42 - W

Now, area = LW

= (42 - W)(W)

= 42W - W² .

For maximum area, first derivative of area becomes zero.

42 - 2W = 0

42 = 2W

W = 21

L = 42 - W

L =42 -21

L = 21

So, L = 21 and W = 21

But if length and breadth are equal then it is a square.

So for rectangle L = 21+1 and W = 21-1

L = 22 and W = 20

Therefore, Length = 22ft and Width = 20ft are the dimensions of plot which maximize the area.