Final answer:
The rectangle with dimensions 10 feet by 10 feet has the smallest perimeter of 40 feet among the given options with an area of 100 square feet.
Step-by-step explanation:
The student has asked which rectangle has the smallest perimeter given that all rectangles have an area of 100 square feet. To find the perimeter of a rectangle, we use the formula perimeter = 2(length + width). The rectangles given in the question are:
- a) 5 feet by 20 feet
- b) 10 feet by 10 feet
- c) 4 feet by 25 feet
- d) 2 feet by 50 feet
We will calculate the perimeter for each of these rectangles:
- For option (a): Perimeter = 2(5 feet + 20 feet) = 2(25 feet) = 50 feet.
- For option (b): Perimeter = 2(10 feet + 10 feet) = 2(20 feet) = 40 feet.
- For option (c): Perimeter = 2(4 feet + 25 feet) = 2(29 feet) = 58 feet.
- For option (d): Perimeter = 2(2 feet + 50 feet) = 2(52 feet) = 104 feet.
Thus, the rectangle with dimensions 10 feet by 10 feet has the smallest perimeter, which is 40 feet.