The width of a house must be 48 feet, but the length (l) can change.what happens to the perimeter (P) of the house when the length changes?

The perimeter of the house is always P=2×48+2×length. We start with length = l

If l changes from l to l+Δl then the perimeter changes from P to P+2Δl

Feel free to make Δl positive or negative or even zero