the three sides of a triangle can be written as:

2x - 1, 2x + 1, 2x + 3, where x is integer, and 2x - 1 > 0 that is x > 1/2 (since the sides are consecutive odd integers)

the perimeter of the triangle is 39 inches:

(2x - 1) + (2x + 1) + (2x + 3) = 39

by solving we find:

x = 6

click here to see the step by step solution of the equation:

2*6 - 1 = 11

2*6 + 1 = 13

2*6 + 3 = 15

the lengths of the sides of the triangle are: 11 in, 13 in and 15 in.