Intermath | Workshop Support

 Write-up

Title
The Third Side

Problem Statement
The lengths of two sides of a triangle are 5 and 11. If the length of the third side is also a whole number, what are the smallest and largest possible perimeters that the triangle can have?

Problem setup

Given the two sides of the triangle, the problem is asking you to find the smallest and largest possible sides of the third side.

Plans to Solve/Investigate the Problem

My initial plan is to use my knowledge of triangle principles to come up with possible solutions for the third side.

Investigation/Exploration of the Problem

When dealing with triangle ABC, A + B must be less than C and C must be greater than A-B.  This is known as the Triangle Inequality Theory.  Because of this and knowing that if 5 is equal to A and 11 is equal to B, C must be greater than 6 and less than 16.  The problem asks us to come up with a whole number.  Since the number has to be less than 16, the highest whole number below 16 is 15.  Using this same reasoning, the lowest number is 7.  To find the perimeter, you must add the lengths of all three sides of the triangle.  Given the two numbers that we have for side C, the largest possible perimeter would be 5+11+15 which is equal to 31.  The smallest possible perimeter would be 5+11+7 which is equal to 23.

Author & Contact
Benjamin Moore
My Email