For each of the following, give at least 5 possible values for the third length so there exists a triangle having these as sidelengths (decimal values could also be chosen): (a) 1, 100 (b) 5, 5 (c) 3, 7. See if you can describe all possible lengths of the third side in each case, so that a triangle exists with those sidelengths. For example, in case (a), all numbers strictly between 99 and 101 would be possible.
Third side must be between 99 and 101 (exclusive). Values: 99.5, 99.8, 100, 100.2, 100.5.
Third side must be between 0 and 10 (exclusive). Values: 1, 3, 5, 7, 9.
Third side must be between 4 and 10 (exclusive). Values: 5, 6, 7, 8, 9.
Explanation
(a) Third side > |100-1| = 99 and < 100+1 = 101. (b) Third side > |5-5| = 0 and < 5+5 = 10. (c) Third side > |7-3| = 4 and < 7+3 = 10.