Final answer:
The side length of a square rug with an area of 42 ft² is the square root of 42, which is an irrational number. Thus, the appropriate answer is c. √42.
Step-by-step explanation:
The question is asking to find the side length of a square rug with an area of 42 ft² and determine if this side length is a rational number. To find the side length a, we can take the square root of the area, because the area of a square is calculated as side length squared (a²).
The side length as a square root is √42. This number is not a perfect square, and when simplified, it will still have the square root sign, which means it cannot be expressed as a fraction of two integers. Therefore, √42 is an irrational number. The options provided are a. 42, b. 84, c. √42, d. √84. The correct side length expressed as a square root is c. √42.