How Long Can It Be?

The same two sides, 6 and 10, also give an upper limit on the third side. If x is longer than 6 and 10 added together, then x is the longest side, and the 6 and the 10 are too short to meet across it. So x must be less than their sum:

x < 6 + 10

x < 16

At x = 16 the 6 and the 10 lie flat along the third side. At 17 they cannot meet at all.

Now you have both limits. The third side must be greater than the difference of the two known sides, the larger minus the smaller, and less than their sum. In the next lesson you will combine the two limits into one inequality.