Question 353399
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The area of the rectangle defined by the outside edge of the lawn is *[tex \Large 270\ \times\ 360\ =\ 97200] square feet.  Since the lawn area and the factory area have to be equal, each is one half of that value, or *[tex \Large 48600].  Let *[tex \Large x] represent the width of the lawn.  Since the lawn goes all the way around the factory, the dimensions of the factor have to be *[tex \Large 270\ -\ 2x] by *[tex \Large 360\ -\ 2x].



So we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (270\ -\ 2x)(360\ -\ 2x)\ =\ 48600]


Multiply the binomials using FOIL, collect like terms, and solve the quadratic for *[tex \Large x].  One of the roots will be too large and therefore extraneous.  The correct answer is the smaller of the two roots.


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