Question

The sides of a triangle are equal to integral numbers of units. two sides are 4 and 6 units long, respectively; what is the minimum value for the triangle's perimeter?

Answer 1

I see it in this way. Suppose the side of 4 units comes as close to the one of 6 units as possible, say on top. The other side would be two units. However, there would be no triangle. We need to 'open' it a bit. Since the sides are integers, the third side can't be 2.00001 units and the next vakue is 3. Then the triangle is 4, 6 and 3 units, so that the perimeter is 6+4+3 = 13 units. Of course, forget about the value of the angles. Clearly is not a right triangle. But no one asks about the angles, so ...