SOLUTION: A 22ft by 30ft rectangular plot is surrounded by a walkway of uniform width. If the area of the walkway is 224ft2, what is the width of the walkway?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A 22ft by 30ft rectangular plot is surrounded by a walkway of uniform width. If the area of the walkway is 224ft2, what is the width of the walkway?      Log On


   



Question 1009864: A 22ft by 30ft rectangular plot is surrounded by a walkway of uniform width. If the area of the walkway is 224ft2, what is the width of the walkway?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the plot is:
+22%2A30+=+660+ ft2
The area of the walkway + plot =
+660+%2B+224+=+884+ ft2
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Let +w+ = the width of the walkway
Adding this width to both sides of
the length and width of the plot:
+%28+22+%2B+2w+%29%2A%28+30+%2B+2w+%29+=+884+
+660+%2B+60w+%2B+44w+%2B+4w%5E2+=+884+
+4w%5E2+%2B+104w+-+224+=+0+
+w%5E2+%2B+26w+-+56+=+0+
I can see by looking at this:
+%28+w+%2B+28+%29%2A%28+w+-+2+%29+=+0+
+w+ can't be negative, so
+w+=+2+
The width of the walkway is 2 ft
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check:
+%28+22+%2B+2w+%29%2A%28+30+%2B+2w+%29+=+884+
+%28+22+%2B+2%2A2+%29%2A%28+30+%2B+2%2A2+%29+=+884+
+%28+22+%2B+4+%29%2A%28+30+%2B+4+%29+=+884+
+26%2A34+=+884+
+884+=+884+
OK