Question 426817
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Let *[tex \Large x] represent the width of the patio.  Then the overall dimensions of the pool including the patio are *[tex \Large 40\ +\ 2x] by *[tex \Large 60\ +\ 2x].  If the area of the patio and the area of the pool are the same, then the area of both of them together must be two times the area of the pool, namely 2 times 2400 or 4800 square feet.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2x\ +\ 60)(2x\ +\ 40)\ =\ 4800]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^2\ +\ 200x\ -\ 2400\ =\ 0]


Solve the quadratic for *[tex \Large x].  It factors.  Discard the negative root.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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