Final answer:
The possible lengths of a side of the rectangle are 5.5 feet.
Step-by-step explanation:
To find the possible lengths of a side of the rectangle, we can use the given information about the perimeter and the area. Let's assume the length of the rectangle is L and the width is W. According to the problem, the perimeter is 44 feet, so we can write the equation: 2L + 2W = 44. Simplifying, we get L + W = 22. Now, let's consider the area. We know that the area of a rectangle is given by the formula A = L x W. The maximum area allowed is 105 square feet, so we can write the inequality: A <= 105. Substituting the formula for A, we get L x W <= 105. Using this information, we can find the possible lengths of a side:
A) 11 feet: If we let L = 11 and W = 11, the equation L + W = 22 is satisfied, and the area L x W = 11 x 11 = 121 square feet is greater than 105. Therefore, this option is not possible.
B) 5.5 feet: If we let L = 5.5 and W = 16.5, the equation L + W = 22 is satisfied, and the area L x W = 5.5 x 16.5 = 90.75 square feet is less than 105. Therefore, this option is possible.
C) 10 feet: If we let L = 10 and W = 12, the equation L + W = 22 is satisfied, and the area L x W = 10 x 12 = 120 square feet is greater than 105. Therefore, this option is not possible.
D) 8 feet: If we let L = 8 and W = 14, the equation L + W = 22 is satisfied, and the area L x W = 8 x 14 = 112 square feet is greater than 105. Therefore, this option is not possible.
Therefore, the possible lengths of a side of the rectangle are B) 5.5 feet.