SOLUTION: 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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 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      Log On


   

Question 88262: 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?
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
THE GARDEN IS 30*40=1200 SQFT. WITH THE WALK WAY THE AREA IS 1800.
SO WITH THE WALKWAY WE HAVE THE FOLLOWING DIMENTIONS:
(30+2W)(40+2W)=1800 WHERE THE 2W IS THE WIDTH OF THE TWO WALKWAY ONE ON EITHER WIDTH & LENGTH.
(30+2W)(40+2W)=1800
1200+80W+60W+4W^2=1800
4W^2+140W+1200-1800=0
4W^2+140W-600=0
4(W^2+35W-150)=0
USING THE QUADRATIC EQUATION WE GET:
W=(-35+-SQRT[35^2-4*1*-150])/2*1
W=(-35+-SQRT1225+600])/2
W=(-35+-SQRT1825)/2
W=(-35+-42.72)/2
W=(-35+42.72)/2
W=7.72/2
W=3.86 FT. ANSWER FOR THE WIDTH OF THE SIDEWALK.