Question

A rectangular rug has an area of 84 square feet. If its length is 2 feet more than twice its​ width, find the dimensions of the rug.
The length of the rug is __. ____. (options for second blank box are feet, square feet, or cubic feet.

Answer 1

L=2W+2

W=(L-2)/2

A=LW, using W from above makes this

A=L(L-2)/2

2A=L^2-2L

L^2-2L-2A=0, given A=84

L^2-2L-168=0

(L-14)(L+12)=0, since L>0

L=14

The length of the rug is 14 ft

(W=(L-2)/2=6 ft)