Question 1161357
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The perimeter of a rectangle is given by *[tex \Large P\ =\ 2l\ +\ 2w] but in this case we know that *[tex \Large l\ =\ 5w\ -\ 3], so the perimeter of your specific rectangle is represented by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P\ =\ 2(5w\ -\ 3)\ +\ 2w]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P\ =\ 12w\ -\ 6]


The correct answer depends on what you mean by "between".  If the perimeter must be in the open interval *[tex \Large (18,90)\ ] then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 18\, yds\ <\ 12w\ -\ 6\ <\ 90\, yds]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 24\, yds\ <\ 12w\ <\ 96\, yds]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\, yds\ <\ w\ <\ 8\, yds]


On the other hand, if your definition of between means that the perimeter must be in the closed interval *[tex \Large \[18,90\]\ ] then just replace the *[tex \Large <\ ] operator with the *[tex \Large \leq\ ] operator



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\, yds\ \leq\ w\ \leq\ 8\, yds]
						
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
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