Question

A triangle has sides of length 7 cm, 4 cm, and 5 cm. How many triangles can be drawn that fit this description?

Answer 1

Answer: 1

Only one triangle can be drawn to fit the description.

Answer 2

It's a goofy question.  These sides satisfy the triangle inequality, 7 < 4+5, so we can draw as many triangles as we care to with those sides.

The more interesting question is how many non-congruent triangles can we draw with those sides?   The answer is only 1, because by SSS all triangles with those sides will be congruent.

If we're asking about how many triangles with these sides cannot be mapped to each other through translation and rotation, the answer is two, basically a pair of reflected copies.

So much for deconstructing this lousy question.  Let's go with

Answer: 1