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?

1 Answer
George C.
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 = (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#

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