If two sides of a triangle have lengths 1 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:   (5-1) &lt; {third side} &lt; (5+1).   4 &lt; {third side} &lt; 6.   Perimeter = {third side} + 1 + 5 = {third side} + 6.   10 &lt; {perimeter} &lt; 12.   answer None
<result>A</result>
If two sides of a triangle have lengths 1 and 5, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19