Question 384604
<font face="Garamond" size="+2">


Let *[tex \Large w] represent the width.  Then *[tex \Large w\ +\ 8] must represent the width.  The area of a rectangle is the product of the width and the length, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w(w\ +\ 8)\ =\ 90]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w^2\ +\ 8w\ -\ 90\ =\ 0]


This doesn't factor, so use the quadratic formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ \frac{-b\ \pm\ \sqrt{b^2\ -\ 4ac}}{2a}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ \frac{-8\ \pm\ \sqrt{64\ +\ 4(1)(90)}}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ -4\ \pm\ \sqrt{106}]


Since we are looking for a positive measure of length, discard the negative root.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ -4\ +\ \sqrt{106}]


Then adding 8 to get the length:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ 4\ +\ \sqrt{106}]


Multiplying the two values to check that the product is indeed 90 is left as an exercise for the student.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>