What is the maximum possible length of y, if y must be an integer?

Question

anonymous · Answer

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mathmate · Answer

Just line in the triangle inequality,  the minimum length of the fourth side of this quadrilateral would be 1<y<3+4+5.

mathmate · Answer

*like

anonymous · Answer

If the figure can be flattened then y = 12, else y = 11, the next smallest integer

anonymous · Answer

Where'd you get those two numbers from? @robtobey

mathmate · Answer

3+4+5=12
But if y=12, it becomes a degenerate quadrilateral with no area (two coincident straight lines).
So it has to be small at least by one so that y stays an integer.
This is equivalent to saying y<3+4+5  so you will understand when you have another quadrilateral.

anonymous · Answer

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anonymous · Answer

Oh, I see...Thank you for your help! @mathmate and @robtobey

anonymous · Answer

You're welcome.

mathmate · Answer

You're welcome!