Question 500340
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The perimeter of a rectangle is given by *[tex \Large P\ =\ 2l\ +\ 2w]


Since you are given a perimeter of 60 cm:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2l\ +\ 2w\ =\ 60]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ l\ =\ 30\ -\ w]


The area of a rectangle is given by *[tex \Large A\ =\ lw]


Since you are given an area of 216 cm² you can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ lw\ =\ 216]


But from the previous steps you can substitute for *[tex \Large l]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (30\ -\ w)w\ =\ 216]


A little algebra music, Sammy:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w^2\ -\ 30w\ +\ 216\ =\ 0]


Solve the quadratic.  The two roots will be your dimensions.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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