Question 399163
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If there are 600 feet of fence, the perimeter must be 600 feet.  So we know that 2 times the length plus 2 times the width is equal to 600.  We also know that length times width equals 19,475 square feet.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2l\ +\ 2w\ =\ 600]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ l\ =\ 300\ -\ w]


And then we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (300\ -\ w)w\ =\ 19475]


And with a little algebra:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -w^2\ +\ 300w\ -\ 19475\ =\ 0]


Which is a tidy little quadratic, quite factorable.  One root is the width, and the other is the length.


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