Answer:
4 < s < 20
Step-by-step explanation:
The triangle inequality requires that any side of a triangle must have a length that is between the difference and the sum of the lengths of the other two sides.
For unknown side s, the length must be ...
(12 -8) < s < (12 +8)
4 < x < 20
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Additional comment
The triangle inequality is usually written ...
a + b > c . . . . . for any assignment a, b, c to side lengths
If s is not the longest side, then we require ...
s +8 > 12 ⇒ s > 4
If s is the longest side, then we require ...
8 +12 > s ⇒ s < 20
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Some authors write the inequality as ...
a +b ≥ c
This allows a "triangle" that looks like a line segment. It will have an area of 0. If your curriculum uses this version of the triangle inequality, then the answer to this question will be 4 ≤ s ≤ 20.
