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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  such that the triangle exists? Separate your answers using commas and express them in increasing order.

 May 18, 2020
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Well, it two sides of a triangle are 7 and 10, the third side must be more than 3  (10 - 7)

and, at the same time, must be less than 17 (7 + 10)

So, you are looking for values of x such that:  3 < x2 < 17.

You'll need to list all the values of x that solve that inequality.

 May 18, 2020

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