SOLUTION: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?      Log On


   

Question 45004This question is from textbook
: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path? This question is from textbook

Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
Let "w" represent the width of the path. After the path has been layed, the new dimensions of the garden area are:
length+=+30+-2w (we must subtract 2w because there is a path at both ends of the lawn),
width+=+20+-2w
Now the area is Area=%2830-2w%29%2820-2w%29
This area is equal to 400 sq ft:
400=%2830-2w%29%2820-2w%29
400=600-60w-40w%2B4w%5E2
0=200-60w-40w%2B4w%5E2
4w%5E2-100w%2B200=0
w%5E2-25w%2B50=0
Now use the quadratic solver w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a = 1
b = -25
c = 50
To give:
w+=%2825+%2B-+sqrt%28+25%5E2-200+%29%29%2F2+++
w+=%2825+%2B-+20.61%29%2F2+++
w+=%2825+%2B-+20.61%29%2F2+++
so w=2.191 or w=22.808.
22.808 ft seems ridiculously wide for a garden path, so the answer must be w=2.191ft.
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam