Answer:
(a) A = W(140 -W)
(b) W = 70
(c) 4900 square yards
Explanation:
You want an expression for the rectangular area that can be enclosed by 280 yards of fence, if that area has width W. Further, you want the value of W that maximizes the area, and the size of that maximum area.
Perimeter expression
The perimeter of the rectangle with length L and width W is ...
P = 2(L +W)
Then the length can be found from the width as ...
L = P/2 -W
For P=280, this is ...
L = 140 -W
(a) Area expression
The area is the product of length and width:
A = LW
A = (140 -W)(W)
(b) Maximum area
The area expression describes a downward-opening parabola with zeros at W=0 and W=140. The vertex (maximum) of the parabola is on the line of symmetry, halfway between these zeros. The value of W there is ...
W = (0 +140)/2 = 70
The area is largest for W = 70.
(c) Area
For that value of W, the area is ...
A = (140 -70)(70) = 70² = 4900 . . . . . square yards
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Additional comment
The generic solution to the area problem when fence is on all sides is that the shape is a square.
If the cost of fence is different for the different sides, the total cost in the east-west direction is equal to the total cost in the north-south direction when cost is minimized.