The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 45?

17

Step-by-step explanation:

Let x be the first side

x+2 is the next side (consecutive odd number)

x+4 is the third side (consecutive odd number)

P = x + x+2 + x+4

45 = x + x+2 + x+4

Combine like terms

45 = 3x+6

Subtract 6 from each side

45-6 = 3x+6-6

39 = 3x

Divide by 3

39/3 = 3x/3

13 = x

The longest side is

x+4

13+4 = 17

The longest side is 17