What is the greatest possible perimeter of an obtuse triangle, each of whose side lengths is a whole number of inches less than or equal to 100?

It is not possible to make an obtuse triangle whose sides are less than or equal to 100. This is because in order to make an obtuse triangle, you have to get a side length that is greater than 100.

It is impossible to construct an obtuse triangles

with all sides less than 100. The reason is that

one of the sides "must" be greater than 100 in

order to the triangle to be obtuse.