A triangle has two sides of length 8 and 18. What compound inequality describes the possible lengths for the third side, x?
Question
A triangle has two sides of length 8 and 18. 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 a triangle with sides of length 8 and 18, we can set up the following inequalities for the third side, x:
- x < 8 + 18
- x > 18 - 8
Solving these inequalities gives:
- x < 26
- x > 10
So, the compound inequality that describes the possible lengths for the third side, x, is 10 < x < 26.
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