Question

If the integer lengths of the three sides of a trinalge are 4, x, and 9, what is the least possible perimeter of the trinalge

Answer 1

The smallest possible triangle will actually contract to a line, where 4+x has to connect to both ends of the side of 9. So 4+x=9, so x=5. The perimeter will then be 4+5+9=18.