# The length of a rectangular piece of carpet is 4 yards greater than the width. How do you express the area of the carpet as a function of the width?

Area (as a fun. of width w) = w^2+4w. sq.yards.
Denote by $w$ the width of the rectangular piece of carpet.
Then, by what is given in the problem, length$= 4 + w i \mathrm{dt} h = 4 + w .$
So the Area = length x width $= \left(4 + w\right) w = {w}^{2} + 4 w$ sq.yrd., as a fun. of width $w$.