Can the sides of a triangle have lengths 5, 14, and 17?

Question

yes or no

Answer 1

The sum of two sides of a triangle must be greater than the third.

Is that true of 5, 14, and 17?

Answer 2

Yes, a triangle can have sides of those lengths. Think of three straight lines (in our case, 5, 14, and 17). Lay the longest side (17 units) flat on the ground. Then lay the shorter sides (5 and 14 units) on top. If the combined length of the two short sides is greater than the length of the longest side, then you can make a triangle.