Why not 4 <= x <= 9?
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Sorry to bother again, but why can't \(x\) be in the range \(4 \leq x \leq 9\)? Having \(4 \leq x \leq 9\) doesn't make a cube, only \(2\) square faces.
Professor Loh is the best mathematician and teacher
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Oh, never mind, I just realized that in the problem, 4 faces of the rectangle are the same, so if \(4 \leq x \leq 9\), we form a cube, not a rectangle.
Professor Loh is the best mathematician and teacher
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Wait, @aaronhma, you're actually right-- if we have a rectangular prism with sides \(4,4,9\), then we actually do have only \(2\) square faces! And the remaining \(4 \text{ x } 9\) faces are all the same, so that's \(4\) rectangular faces with the same ratio of length to width.
That's a really good catch you made there! It never specified which of the \(4\) faces had the same ratios, so making it \(4 \leq x \leq9\) is actually reasonable.
BUT, since the problem says that \(4\) is the smallEST dimension, and that \(9\) is the longEST, it doesn't really make sense for the dimensions to be \(4,4,9\), because then there is no smallEST dimension, just two smaller lengths. So that's another way to think about it using the wording in the problem
