Question

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?

Answer 1

`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 = (n-2) + n + (n+2) = 3n`

Hence `n = 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`