Question 566791
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You are not "only given the area...", you are also given that *[tex \Large h] is 7 more than *[tex \Large w].


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ h\ =\ w\ +\ 7]


You also know that the area is given by *[tex \Large A\ =\ hw], so substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A(w)\ =\ (w\ +\ 7)w]


And with the given value for area:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w^2\ +\ 7w\ =\ 330]


Put it in standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w^2\ +\ 7w\ -\ 330\ =\ 0]


Solve the quadratic (it factors, 22 and 15 have a difference of 7, hmmm), discard the negative root.  The positive root is *[tex \Large w] and *[tex \Large h] is 7 more than that.


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