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# Help!

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The lengths of the sides of a non-degenerate triangle are $x$, 13 and 37 units. How many integer values of $x$ are possible?

Aug 16, 2019

$$\text{We must have the sum the lengths of any two sides greater than the length of the third side}\\ x+13> 37\\ 13 + 37 > x\\ 24 < x < 50\\ x \in \{25, 26, 27, \dots 49\}\\ \text{There are 25 integer values of x}$$