SOLUTION: A 17ft. by 33ft. rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216ft. squared, how wide is the walkway?

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Question 1017223: A 17ft. by 33ft. rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216ft. squared, how wide is the walkway?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Study this demonstration, which is the same kind of form as your question:

rectangular outside border of uniform width, find uniform width
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A 17ft. by 33ft. rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216ft. squared, how wide is the walkway?
----------------------------------- 

Let x = the width of the walkway.

Then you have this equation to determine x:

(17 + 2x)*(33 + 2x) - 17*33 = 216.

Do you understand why it is your equation to determine x?
Because it is the difference of the areas of two rectangles.

OK. Now let us solve it. Open the parentheses, and you will get

 -  = ,   or

 = ,   or

 = ,   or dividing by 4 both sides

 = ,

Factor the left side

 = (x-2)*(x+27).

So the roots of the last quadratic equation are 2 and -27.

Only positive x = 2 suits.

Answer. The width of the walkway is 2 ft.


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