The width, w, of a rectangular rug is 4 less than its length, L. If the perimeter of the rug is 120 square feet, which equation could be used to find the dimensions of the rug?

a. L (4-L) = 120

b. L (L-4) = 120

c. 2 (L-4) + 2L = 120

d. 2 (4-L) + 2L = 120

Answer: The correct answer is option C; 2 (L-4) + 2L = 120

Step-by-step explanation: First of all we need to identify the variables and these are L, which is the length and W which is the width. The width is 4 less than the length of the rectangular rug. That means if the length is L, the width would be L - 4.

Also the perimeter has been given as 120. Note also that the perimeter is calculated as follows;

Perimeter = 2 (L + W)

Substituting for the known values we now have;

120 = 2 (L + L - 4)

120 = 2L + 2L - 8

Rearranging the right hand side now gives us

120 = 2L + (2L - 8)

120 = 2L + 2 (L - 4)

(Note that this is the same as in option C, but the left hand side of the equation is now on the right hand side, and vice versa)