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?

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Let "w" represent the width of the path. After the path has been layed, the new dimensions of the garden area are:
(we must subtract 2w because there is a path at both ends of the lawn),

Now the area is
This area is equal to 400 sq ft:





Now use the quadratic solver
where
a = 1
b = -25
c = 50
To give:



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