Lucy bought 162 feet of fencing with which to enclose a rectangular garden. of the lengths of the garden's sides are whole numbers, what is the maximum number of square feet she can enclose with the fencing?

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18 December, 13:36

Lucy bought 162 feet of fencing with which to enclose a rectangular garden. of the lengths of the garden's sides are whole numbers, what is the maximum number of square feet she can enclose with the fencing?

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Montana · Answer 1

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.

Adalyn Sims · Answer 2

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