A triangle has two sides of length 16.2 and 16.3. What compound inequality describes the possible lengths for the third side, x?
Question
A triangle has two sides of length 16.2 and 16.3. What compound inequality describes the possible lengths for the third side, x?
Solution
The possible lengths for the third side, x, of a triangle with two sides of lengths 16.2 and 16.3 can be described by the triangle inequality theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the absolute difference of the lengths of the other two sides.
So, the compound inequality that describes the possible lengths for the third side, x, is:
|16.2 - 16.3| < x < 16.2 + 16.3
Solving the absolute value inequality gives:
|-0.1| < x < 32.5
So, the compound inequality is:
0.1 < x < 32.5
This means that the length of the third side of the triangle must be greater than 0.1 and less than 32.5.
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