Final answer:
To find the smallest rectangle with an area of 400 square feet, pair the factors closest together to find the smallest perimeter.
Step-by-step explanation:
To find the dimensions of the smallest rectangle with an area of 400 square feet, we need to find the factors of 400 that will give us the smallest possible values. The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, and 50. We can pair these factors to find the dimensions.
For example, if we pair 1 and 400, we get a rectangle with dimensions 1 by 400. However, this is not the smallest possible rectangle because the perimeter is 802, which is larger than the perimeter of some other pairings. To find the smallest perimeter, we need to pair the factors that are closest together.
If we pair 20 and 20, we get a rectangle with dimensions 20 by 20. The perimeter of this rectangle is 80, which is the smallest possible perimeter among the pairings of factors. Therefore, the smallest rectangle that can be constructed with an area of 400 square feet has dimensions 20 feet by 20 feet, and a perimeter of 80 feet.