The area of a rectangular wall of a barn is 198 square feet Its length is 4 feet longer than twice its width

L=2W+4 L is the length and W is the width.
W(2W+4)=198

2W^2+4W-198=0

2(W^2+2W-99)=0

2(W+11)(W-9)=0

W-9=0

W=9 feet is the width. 

L=2*9+4=18+4=22 and is the length.

Proof: 

9*22=198

198=198 -Jerry