Find the greatest possible length of the height of the trapezoid, if the perimeter of the trapezoid is 6

Answer 1

If the height is 3, then each base has length zero, since the two sides must each b e 3.
So, make the height just a bit less than 3, say, 3-x, and the two bases can have very small lengths which must add to less than 2x.

Answer 2

So what would the answer be ?