Ed's final revision doesn't quite do the job.

That rather depends on what the job is.

Absent further context, I think it would be OK to assume that the job is to specify

__which__ triangle is on the right.

The flaw in the original might not matter, and it might not be necessary to make clear how many 3-inch sides the triangle in question has.

Suppose there are three triangles to choose from, and of all the nine sides only one is 3 inches long. Then there is no problem.

If two (or three) of the nine sides are that length, and both (or all) of them belong to the same triangle, then this version would

__still__ do the job, but of course it sounds wrong to say "the triangle with

__the__ 3 inch side" when in fact it has two or three 3-inch sides. It would be better then to say "with the 3-inch side

**s**".

If two (or three) of the nine sides are that length, and they are both (all) on different triangles, the description obviously would not work.

If one triangle has

__one__ 3-inch side, and one or both of the other triangles have two or more, then this is the case in which your addition of 'exactly' would help.