Answer:
- 5 < x < 21
- 12.1 < x < 35.1
- 7 < x < 37
- 6.5 < x < 19.9
- 21 < x < 67
Explanation:
Given pairs of side lengths that represent two sides of a triangle, you want an inequality representing possible lengths for the third side.
Triangle inequality
The triangle inequality requires the sum of the two shortest sides be greater than the longest side. Translated to this problem, it means the third side must have a length between the difference and the sum of the other two sides. For third side x, we require ...
a. 8 and 13
13 -8 < x < 13 +8
5 < x < 21
b. 11.5 and 23.6
23.6 -11.5 < x < 23.6 +11.5
12.1 < x < 35.1
c. 22 and 15
22 -15 < x < 22 +15
7 < x < 37
d. 13.2 and 6.7
13.2 -6.7 < x < 13.2 +6.7
6.5 < x < 19.9
e. 23 and 44
44 -23 < x < 44 +23
21 < x < 67
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