Final answer:
By using the perimeter formula for a rectangle and substituting the given relationship between length and width, we find that the width of the rectangle is 7 cm.
Step-by-step explanation:
The problem at hand is to find the width of a rectangle where the perimeter is given to be 56 cm, and the length is known to be three times its width. The formula for the perimeter of a rectangle is P = 2l + 2w, where P represents the perimeter, l is the length, and w is the width. In this case, the length (l) can be denoted as 3w since it's three times the width. So, the equation becomes 56 = 2(3w) + 2w, which simplifies to 56 = 6w + 2w. Combining like terms gives us 56 = 8w. Dividing both sides by 8 yields w = 7. Therefore, the width of the rectangle is 7 cm, which corresponds to option C.