Question 190806
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Let <i><b>x</b></i> represent the width of the margin.  Then the height of the printed area has to be  <b>20 - 2<i>x</b></i> and the width has to be <b>16 - 2<i>x</b></i>.  The <i><b>x</b></i> is multiplied by 2 because there is a margin on the top and another on the bottom, each of width <i><b>x</b></i>.  Left and right, same thing.  The area covered must be *[tex \LARGE 192\text{ cm^2}], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  (20 - 2x)(16 - 2x) = 192]


Apply FOIL


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  320 - 72x + 4x^2 = 192]


Put in standard form


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  4x^2 - 72x + 128 = 0]


Divide by common factor


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x^2 - 18x + 32 = 0]


Factor


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  (x - 16)(x - 2) = 0]


Apply Zero Product Rule


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = 16\text{ cm}] or *[tex \LARGE x = 2\text{ cm}]


But before you go off willy-nilly and submit both of those answers, let's think about this.  If the page is only *[tex \LARGE 16\text{ cm}] wide to begin with, how could the margin on each side be *[tex \LARGE 16\text{ cm}]?  Extraneous root -- exclude it and go with the more reasonable (and correct) *[tex \LARGE 2\text{ cm}] .


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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