SOLUTION: This is a word problem that I am stuck on. I have a rectangular garden with dimensions of 30' by 40'. The total garden area is 1800 ft^2. I am trying to figure the constant width o

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: This is a word problem that I am stuck on. I have a rectangular garden with dimensions of 30' by 40'. The total garden area is 1800 ft^2. I am trying to figure the constant width o      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 50760This question is from textbook
: This is a word problem that I am stuck on. I have a rectangular garden with dimensions of 30' by 40'. The total garden area is 1800 ft^2. I am trying to figure the constant width of the surrounding walkway. I came up with area = (40-2x)*(30-2x)=1800, 800-80x-60x+4x^2=1800 please help, thanks This question is from textbook

Answer by stanbon(48546) About Me  (Show Source):
You can put this solution on YOUR website!
I have a rectangular garden with dimensions of 30' by 40'. The total garden area is 1800 ft^2. I am trying to figure the constant width of the surrounding walkway.
-----------
If the garden is 30 x 40 its area is 1200 sq ft.
The 1800 sq ft must refer to the garden area plus
the area of the sidewalk which surrounds the garden
area.
The sidewalk area must be 600 sq. ft.
-----------------------
Draw the picture. The sidewalk is composed of four
rectangles.
TWO are (40+2x)*x each or a total of 2x(40+2x) sq ft.
The other TWO are 30 * x each or a total of 2(30x)=60x sq. ft.
EQUATION:
2x(40+2x)+60x=600
80x+4x^2+60x=600
4x^2+140x-600=0
x^2+35x-150=0
x=[-35+sqrt(35^2-4(-150)]/2
x=3.86 ft. (width of the sidewalk.
Cheers,
Stan H.