here is an example you can learn from.
#1: Is it possible to form a triangle with the given side lengths? If not, explain why not. 1. 5 cm, 7 cm, 10 cm SOLUTION: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5 ANSWER: Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5
2. 3 in., 4 in., 8 in. SOLUTION: No; . The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ANSWER: 3+4*8
3. 6 m, 14 m, 10 m SOLUTION: Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6 . The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. ANSWER: Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6
4. MULTIPLE CHOICE If the measures of two sides of a triangle are 5 yards and 9 yards, what is the least possible measure of the third side if the measure is an integer? A 4 yd B 5 yd C 6 yd D 14 yd SOLUTION: Let x represents the length of the third side. Next, set up and solve each of the three triangle inequalities. 5 + 9 > x, 5 + x > 9, and 9 + x > 5 That is, 14 > x, x > 4, and x > –4. Notice that x > –4 is always true for any whole number measure for x. Combining the two remaining inequalities, the range of values that fit both inequalities is x > 4 and x < 14, which can be written as 4 < x < 14. So, the least possible measure of the third side could be 5 yd. The correct option is B. ANSWER: B