Final answer:
To solve for the length and width of a rectangle with a perimeter of 84 cm using the formula P = 2l + 2w, additional information is required. Without a given length or width, we can only express one dimension in terms of the other.
Step-by-step explanation:
To find the length and width of a rectangle with a known perimeter, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Since the perimeter is given as 84 cm, we can set up the equation 84 = 2l + 2w. However, we need additional information to find the exact dimensions because there are infinitely many length-width combinations that could result in a perimeter of 84 cm. If we had either the length or the width, we could substitute it into the equation and solve for the other dimension. Without such information, we can only express the length in terms of width or vice versa, for example, l = 42 - w.
Since the question seems to suggest a unit scale or ratio is involved but does not provide enough context or specific values to create a concrete equation.