Question 254502
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Let *[tex \Large x] represent the measure of one of the sides.  Let *[tex \Large w] represent the measure of an adjacent side.


The perimeter, *[tex \Large P], of a rectangle is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P\ =\ 2l\ +\ 2w]


Where *[tex \Large l] is the measure of the length and *[tex \Large w] is the measure of the width].


Solving the equation for *[tex \Large w] we get:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ =\ \frac{P\,-\,2l}{2}]


So, if in the given rectangle, *[tex \Large x] represents the length and the perimeter is 20, then the width of the rectangle would be represented by *[tex \Large \frac{20\,-\,2x}{2}]


The Area of a rectangle is given by the length times the width, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A(x)\ =\ \left(\frac{20\,-\,2x}{2}\right)x\ =\ \frac{20x\,-\,2x^2}{2}\ =\ 10x\ -\ x^2]



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