If two sides of a triangle have lengths 3 and 5, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19  Choose one
A) None	B) I only	C) II only	D) II and III only	E) I, II, and III
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:   (5-3) &lt; {third side} &lt; (5+3).   2 &lt; {third side} &lt; 8.   Perimeter = {third side} + 3 + 5 = {third side} + 8.   10 &lt; {perimeter} &lt; 16.   Answer: II only.
<result>C</result>
If two sides of a triangle have lengths 3 and 5, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19