<PRE><B>Question 191722</B>
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First thing, you do this one in your head.  5 - 12 - 13 is a Pythagorean Triple and 5 and 12 differ by 7.  Therefore the width is 5 and the length is 12.


But since you have to have an equation and name the variables...


Let &lt;i&gt;&lt;b&gt;x&lt;/b&gt;&lt;/i&gt; represent the width.


Then &lt;i&gt;&lt;b&gt;x&lt;/b&gt;&lt;/i&gt;&lt;b&gt; + 7&lt;/b&gt; has to be the length.


Since the diagonal of a rectangle forms a right triangle with the the length and the width, Pythagoras tells us you can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + (x + 7)^2 = 13^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + x^2 + 14x + 49 = 169]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2 + 14x - 120 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + 7x - 60 = 0]


Factor and solve for x.  Exclude the extraneous negative root.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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