SOLUTION: A rectangular swimming pool 12m by 8m is surrounded by a concrete path of uniform width. If the area is 224m^2, find its width

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Question 1038000: A rectangular swimming pool 12m by 8m is surrounded by a concrete path of uniform width. If the area is 224m^2, find its width
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Draw and label the rectangular figure. 
x     one of the pool's dimensions
y     the other pool's dimensions
w     uniform width extending from the two dimensions
A     Area of, ASSUMING the path and the pool combined
      (Your description does not specify which.)
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x=12
y=8
A=224
w=unknown


highlight_green%28%28x%2B2w%29%28y%2B2w%29=A%29-----Solve for w.

xy%2B2yw%2B2xw%2B4w%5E2=A
4w%5E2%2B%282x%2B2y%29w%2Bxy=A
4w%5E2%2B%282x%2B2y%29w%2Bxy-A=0
-
Formula for general solution of quadratic equation gives
w=%28-%282x%2B2y%29%2B-+sqrt%28%282x%2B2y%29%5E2-4%2A4%2A%28-A%29%29%29%2F%282%2A4%29

w=%28-2x-2y%2B-+sqrt%284x%5E2%2B8xy%2B4y%5E2%2B16A%29%29%2F%282%2A4%29

w=%28-2x-2y%2B-+2%2Asqrt%28x%5E2%2B2xy%2By%5E2%2B4A%29%29%2F%282%2A4%29

highlight%28w=%28-x-y%2B-+sqrt%28x%5E2%2B2xy%2By%5E2%2B4A%29%29%2F4%29
If neither of these two values work, then the other assumption may be what you really want; that the "area" is for JUST the concrete path. That would change the initial equation a bit.