Question 54449: 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, garden plus walkway, is to be 1800 ft2. What must be the width of the walkway to the nearest thousandth?
After working the problem I came up with 3.860 ft and then after re working it because it looked wrong I cam up with 5.430 ft. Can you please help?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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, garden plus walkway, is to be 1800 ft2. What must be the width of the walkway to the nearest thousandth?
:
After working the problem I came up with 3.860 ft and then after re working it because it looked wrong I cam up with 5.430 ft.
:
It has to be obvious to you that these high value numbers cannot be right. The walk-way will be only a few feet. Here is how to do it:
Draw a rough diagram of this, labeling the the garden dimensions, and the width of the walk-way as x. Notice that the dimensions of the the total area would be: (2x+30) by (2x+40)
:
The area equation would be:
(2x+30) * (2x+40) = 1800
:
FOIL the two factors:
4x^2 + 80x + 60x + 1200 = 1800
:
4x^2 + 140x + 1200 = 1800
:
4x^2 + 140x + 1200 - 1800 = 0
:
4x^2 + 140x - 600 = 0; our old friend the quadratic equation
:
We can simplify this considerably by dividing all terms by 4, we then have:
x^2 + 35x - 150 = 0
:
This does not factor; use the quadractic formula to find x: a=1; b=35; c=-150
:
The two solutions will be +3.86 and -38.86, only the positive solution makes any sense.
:
The walk-way will be 3.86 ft wide
:
We can check this.
width: 2x + 30 = [2(3.86) + 30] = 7.72 + 30 = 37.72
length: 2x + 40 = [2(3.86) = 40] = 7.72 + 40 = 47.72
:
Area = 37.72 * 47.72 = 1799.998 ~ 1800, the given area
;
Did this make sense to you??
|
|
|
