Question

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

Answer 1

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

Answer 2

*like

Answer 3

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

Answer 4

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

Answer 5

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.

Answer 6

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

Answer 7

You're welcome.

Answer 8

You're welcome!