Final answer:
The side length of a square rug with an area of 121 ft² is found by taking the square root of 121, which is 11. Therefore, the rug has a side length of 11 ft, which makes it a rational number.
Step-by-step explanation:
To find the side length of a square rug with an area of 121 ft2, you would take the square root of the area. The formula for the area of a square is Area = side length x side length, or A = a², where A represents the area and a represents the side length. Since we know the area is 121 ft2, we are looking for the value of a such that a² = 121. Taking the square root of both sides, we find that a = √121.
Now, √121 is equal to 11 because 11 multiplied by itself (11 x 11) gives 121. So, the side length of the square rug is 11 ft. Since 11 is a whole number, it is a rational number. Thus, the side length of the rug is 11 ft, and this length is a rational number.