Question

You're given two side lengths of 6 centimeters and 9 centimeters. Which measurement can you use for the length of the third side to construct a valid triangle?

Answer 1

This answer has to be 15 or less because the two shorter sides added together have to be longer than or equal to the longest side. It also has to be longer than 3 because otherwise, the sides wouldn't reach each other. So, therefore, the side must be longer than three centimeters, but shorter than 15.

Answer 2

-- If the third side is longer than 15 cm, then the 6 and the 9 together
can't reach its ends.

-- If the third side is shorter than 3 cm, then IT can't reach the ends
of the 6 and the 9.

-- So the third side must be longer than 3cm AND shorter than 15 cm.

                     3cm < S < 15cm