let

l = the length of the room, l>0

w = the width of the room, w>o

A rectangular room, that is 5 feet longer than it is wide, is to be carpeted:

l = w + 5

the area of the room is A = length*width

A = l*w plug l = w + 5

A = (w + 5)*w

the carpet costs $20 per square foot thus the total cost will be 20*A dollars or:

20(w + 5)*w = 6000

by solving we find

w = 15 ft

click here to see the step by step solution of the equation

l = 15 + 5

l = 20 ft

the dimensions of the room are: the length is 20 ft and the width is 15 ft.