Question 361782
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The area of a rectangle is the length times the width.  *[tex \Large A\ =\ lw]


The perimeter of a rectangle is 2 times the length plus 2 times the width.  *[tex \Large P\ =\ 2l\ +\ 2w]


Let's use the area formula to develop an expression for length in terms of the width:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ lw\ =\ 363]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ l\ =\ \frac{363}{w}]


Now substitute into the Perimeter formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\left(\frac{363}{w}\right)\ +\ 2w\ =\ 88]


Now multiply through by w:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 726\ +\ 2w^2\ =\ 88w]


Put the quadratic in standard form and divide by 2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w^2\ -\ 44w\ +\ 363\ =\ 0]


Solve for *[tex \Large x].  One root will be the width and the other the length.



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