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A triangle has three sides of the following side lengths: 7, 10, and \(x^2\). What are all of the positive integer values of x such that the triangle exists? Separate your answers using commas and express them in increasing order.

 Jul 25, 2019
 #1
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\(\text{The key thing is that the sum of the length of any two sides is greater than the length of the third side}\\ 7+10 > x^2\\ 17>x^2\\~\\ x^2+7>10\\ x^2 > 3\\ \text{integer values of $x$ are $2,3,4$}\)

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 Jul 25, 2019
 #2
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Thanks Rom! 

 Jul 25, 2019

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