1. ## equation set up

I am having a problem setting up this problem and being successful at solving it.
A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, plus garden walkway, is to be 1800ft^2. What must be the width of the walkway to the nearest thousandth.
I thought A= L X W.
But I am still stuck and do not get a successful answer.

2. Hello, lizard4!

A rectangular garden is to be surrounded by a walkway of constant width.
The garden's dimensions are 30 ft by 40 ft.
The total area, plus garden walkway, is to be 1800 ft².
What must be the width of the walkway to the nearest thousandth.
I hope you made a sketch . . .
Code:
      : x : - -40 - - : x :
*-------------------* - -
x |                   |   :
|   *-----------*   |   :
|   |           |   |   :
30|   |30         |   | 30+2x
|   |    40     |   |   :
|   *-----------*   |   :
x |                   |   :
- *-------------------* - -
: - - - 40+2x - - - :

The garden itself is 30 × 40 ft.
The walkway is $x$ feet wide . . . all the way around.

The entire region has length $(40 + 2x)$ and width $(30 + 2x)$.

There is our equation: . $(40 + 2x)(30 + 2x) \;=\;1800$

3. A = L x W is formula for area of a rectangle, alright.

Which rectangle here?

One rectangle is the 30ft by 40ft garden.
Another rectangle is that garden that is surrouded by walkways of constant width.

If c = constant width of the walkways, the other rectangle is
(30 +2c) by (40 +2c)
whose area is 1800 sq.ft.

So,
(30 +2c)x(40 +2c) = 1800
30*40 +30*2c +2c*40 +2c*2c = 1800

("*" is x or times or multipllied by.)

1200 +60c +80c +4c^2 = 1800
4c^2 +140c +1200 -1800 = 0
4c^2 +140c -600 = 0
Divide both sides of the equation by 4,
c^2 +35c -150 = 0

Cannot factor that. Use the Quadtratic formula,
c = {-35 +,-sqrt[35^2 -4(1)(-150)]} / 2(1)
c = {-35 +,-sqrt[1825]} / 2
c = {-35 +,-42.72001873} /2
c = -38.860 ft, or 3.860 ft.

Reject the -38.860 ft because there are no negative dimensions.

Therefore, the constant width of the walkways is 3.860 ft. ------answer.

check,
(3.860)[(30+3.860+3.860)*2 +(40*2)] + 30*40 =? 1800
600 +1200 =? 1800
1800 =? 1800
Yes, so, OK.