Question 645496
<font face="Times New Roman" size="+2">


Let *[tex \LARGE x] represent the measure of the base of the triangle.  Then the measure of the height must be *[tex \LARGE 2x\ +\ 2].  Since we know that the area of a triangle is the measure of the base times the measure of the height divided by 2, we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x(2x\ +\ 2)}{2}\ =\ 42]


Which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x(x\ +\ 1)\ =\ 42]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ x\ -\ 42\ =\ 0]


Solve the factorable quadratic for the positive root (discard the negative root because we are looking for a measure of length for which negative values are absurd).  Once you have a value for *[tex \LARGE x], calculate *[tex \LARGE 2x\ +\ 2]


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>