Question

The lengths of the sides of a triangle are consecutive odd integers. If the perimeter is 1 less than 4 times the shortest side, find the length of each side

Answer 1

Let the shortest side be x.  Then the other two sides will be x+1 and x+2.

Perimeter = P = sum of the lengths of all three sides = x  +  (x+1) + (x+2) 

This perimeter = 4x -1 (1 less than 4 times the shortest side).

Then x + x + 1 + x + 2 = 4x - 1
      or:        3x + 3         = 4x -1                 Subtr. 3x from both sides:
                                                                  3 = x - 1

x=4, x+1=5, and x+2=6

The 3 sides have lengths 4, 5 and 6.