The plans for a rectangular deck call for the width to be 4 feet less than the length. Sam wants the deck to have an overall perimeter of 52 feet. What should the length of the deck be?

Since rectangles have two pairs of equal-length sides, for any rectangle with length L and width W, its perimeter is always 2L + 2W (or 2 (L + w), whichever you prefer). Here, we're told that the width is 4 feet less than the length. Symbolically, we'd say that W = L - 4. This allows us to write the perimeter entirely in terms of length if we replace our W with the expression on the right side:

2L + 2W = 2l + 2 (L - 4) = 2L + 2L - 8 = 4L - 8

Sam wants this expression to come out to 52, so we can set up the equality 4L - 8 = 52 and solve for L to find what the length has to be:

Adding 8 to either side, the equality becomes 4L = 60. Diving either side by 4 gives us L = 15, which tells us that the length of the deck should be 15 feet.