1)) A triangle has two sides of length 1.2 and 17.8. What compound inequality describes
the possible lengths for the third side, ?
Write a compound inequality like .
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To determine the possible lengths for the third side of a triangle with two sides measuring 1.2 and 17.8, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. Thus, we have two inequalities to set up:

Combining the inequalities that affect , we have:

Therefore, the compound inequality that describes the possible lengths for the third side is .