Lucy bought 162 feet of fencing with which to enclose a rectangular garden. of the lengths of the garden's sides are whole numbe
rs, what is the maximum number of square feet she can enclose with the fencing?
2 answers:
The maximum area would be a square so we need the length and width to be as close as possible to a square. The perimeter is 162 so we have:-
2L + 2W = 162
L + W = 81
so the length will be 41 and width will be 40
So greatest area she can enclose = 40*41 = 1640 ft^2
The rectangle that uses it's perimeter to enclose the most area is a square.
If the perimeter is 162 ft, then each side of the square is
162 / 4 = 40.5 ft.
The area is
(40.5) x (40.5) = 1,640.25 square feet.
If the sides have to be whole numbers, then the closest she can get is 40 ft x 41 ft.
The area is 1,640 square feet.
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