Two sides of a triangle measure 39cm and 15cm. Write and solve an absolute value inequality stating the possible lengths of the third side. State the solution set and graph.

minniedo  Sep 23, 2018

legs of a triangle a, b, c


the triangle inequality states


\(|a|+|b| >|c| \\ \text{with strict inequality else we'd just have a line segment, not a triangle.}\)


\(|c| < |39|+|15| = 54 \Rightarrow c < 54 \\ \text{we also must have }\\ |c|+|15| > 39 \Rightarrow c > 24 \text{ thus}\\ 24 < c < 54 \)

Rom  Sep 23, 2018

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