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A triangle has two sides of length 18.1 and 16.6. What compound inequality describes the possible lengths for the third side, x?​

User Landweber
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1 Answer

1 vote

Answer:

1.5 < x < 34.7

Explanation:

You want a compound inequality describing possible lengths (x) for the third side of a triangle with sides 18.1 and 16.6.

Triangle inequality

The shortest side cannot be any shorter than the difference of the two known sides:

18.1 -16.6 = 1.5

The longest side cannot be any longer than the sum of the two known sides:

18.1 +16.6 = 34.7

The possible lengths of the third side are given by ...

1.5 < x < 34.7

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Additional comment

If the third side is exactly equal to the sum or the difference, then the "triangle" looks like a line segment. It has zero area. That possibility is usually disallowed. If you want to allow it, then change < to ≤ in the inequality.

User Thomas Adrian
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7.5k points