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

Oct 20, 2016

$17$ inches

#### Explanation:

We can convert this into a slightly more abstract problem as follows:

• For "perimeter" we can read "sum"

• For "lengths of the sides of a triangle" we can read "three numbers"

If the middle of the three consecutive odd integers is $n$, then the smallest is $n - 2$, the largest is $n + 2$ and we have:

$45 = \left(n - 2\right) + n + \left(n + 2\right) = 3 n$

Hence $n = \frac{45}{3} = 15$ and the largest of three numbers (i.e. the length of the longest side of the triangle in inches) is $n + 2 = 15 + 2 = 17$