A triangle has two sides of length 8.9 and 1.9. What compound inequality describes the possible lengths for the third side, x?
Question
A triangle has two sides of length 8.9 and 1.9. What compound inequality describes the possible lengths for the third side, x?
Solution
The possible lengths for the third side of a triangle, given two sides, can be found using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
Given the lengths of two sides as 8.9 and 1.9, we can set up the following inequalities:
- x < (8.9 + 1.9)
- x > (8.9 - 1.9)
Solving these gives:
- x < 10.8
- x > 7
So, the compound inequality that describes the possible lengths for the third side, x, is 7 < x < 10.8.
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