Answer:
Explanation:
You want possible dimensions of a field that is 280 square meters in area and has a 3-sided perimeter of 54 meters or less.
Definitions
For the purpose here, we can define the length of the field as the distance parallel to the river. Then the width is the distance out from the river.
Dimensions
Possible whole-number dimensions of the field can be found by considering factor pairs of 280. Listing length first, we could have ...
280 = (280)(1) = (140)(2) = (70)(4) = (56)(5) = (40)(7) = (35)(8) = (28)(10) = (20)(14) . . . and the reverse of these
Perimeter fence
The length of the fence required will be the length plus 2 times the width. For the factor pairs shown, the fence lengths, respectively, are ...
282, 144, 78, 66, 54, 51, 48, 48, 54, 66, 78, 87, 117, 144, 282, 561 . . . meters
The highlighted values are 54 meters or less, corresponding to dimensions ...
- 40 m × 7 m
- 35 m × 8 m
- 28 m × 10 m
- 20 m × 14 m
- 14 m × 20 m
Possible dimensions are 40 m by 7 m, and 28 m by 10 m.
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Additional comment
As you have noted, other values of dimensions are possible, for example, 22.4 m × 12.5 m, a size requiring a fence 47.4 m long.