# Word Problem-Find the Length

#### wallee

##### New member
The length of a rectangular dog pen is 4 feet more than the twice the width. If the total area of the pen is 240 feet, find the length.

I solved it and I got 30 for the Length but the answer in the book is 24. This is how I solved: A=LW so 240=(4L)(2W) I then divided both sides by 2 to eliminate the W and solve for L. So then I got 120=4L then I divided both sides by 4 to solve for L and I get L=30. Apparently thats not the answer. 24 is. Please help if you can solve this problem. Thank You soo Much!

#### skeeter

##### Senior Member
wallee said:
The length of a rectangular dog pen is 4 feet more than the twice the width. If the total area of the pen is 240 square feet, find the length.
L = 4 + 2W

LW = 240

substitute (4 + 2W) for L in the area equation ...

(4 + 2W)W = 240

distribute ...

2W[sup:1y8abg9j]2[/sup:1y8abg9j] + 4W = 240

divide every term by 2 ...

W[sup:1y8abg9j]2[/sup:1y8abg9j] + 2W = 120

W[sup:1y8abg9j]2[/sup:1y8abg9j] + 2W - 120 = 0

factor ...

(W + 12)(w - 10) = 0

W = 10 is the only solution that makes sense in the context of the problem (the width can't be -12 ft)

L = 4 + 2W = 4 + 2(10) = 24

#### wallee

##### New member
THANK YOU SOOOOOOO MUCH SKEETER