If two sides of a triangle have lengths 6 and 10, which of the following could be the perimeter of the triangle?
I. 10
II. 15
III. 25	Choices: A) I only B) II only C) II and III only D) I, II, and III E) none
The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Therefore:   (10-6) &lt; {third side} &lt; (10+6).   4&lt; {third side} &lt; 16.   Perimeter = {third side} + 4 + 16= {third side} + 20.   24 &lt; {perimeter} &lt; 36   Answer: none.
<result>E</result>
If two sides of a triangle have lengths 6 and 10, which of the following could be the perimeter of the triangle?
I. 10
II. 15
III. 25