If two sides of a triangle have lengths 3 and 8, which of the following could be the perimeter of the triangle? I. 9 II. 15 III. 19
Options.
A) None B) I only C) II only D) 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:   (8-3) &lt; {third side} &lt; (8+3).   5 &lt; {third side} &lt; 11.   Perimeter = {third side} + 8 + 3 = {third side} + 11.   16 &lt; {perimeter} &lt; 22.   answer III only
<result>D</result>
If two sides of a triangle have lengths 3 and 8, which of the following could be the perimeter of the triangle? I. 9 II. 15 III. 19