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Cecora Y. A. 5 < x < 10 B. 10 < x < 15 C. 0 < x < 15 D. 5 < x < 15
1 Expert Answer
Hi Cecora Y.
The Triangle Inequality Theorem will help you please look for it in your text or online
The sum of any two sides of a triangle must be greater than the measure of the third side.
Since your sides sum to 15, then your third side must be less than 15 in order for your triangle to close.
I like choice C because if encompasses the other choices, and says that whatever x is it must be less than 15. X could be for example be 14 instead of 6 or 9. With choice C you could have an Isosceles triangle with two sides equal to 10 where 10 + 10 is greater than 5 but two sides equal to 5 each does not allow the triangle to close.
I hope this helps.