The perimeter of a triangle is 187 inches. If one side of the triangle is 12 more than the shorter side, and the longer side is 34 more than the shorter side, find the lengths of the three sides?

P = a + b + c

a = shorter side

b = a + 12

c = a + 34

187 = a + (a + 12) + (a + 34)

187 = 3a + 46

187 - 46 = 3a

141 = 3a

141/3 = a

47 = a

b = a + 12 = 47 + 12 = 59

c = a + 34 = 47 + 34 = 81

lengths of 3 sides are : 47 in, 59 in, 81 in