Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem2

11&12 Video Solutions 2010 problem2

Video Transcription

Video Summary

The problem involves finding triangles with integer side lengths that sum up to a perimeter of seven. Several combinations of integers that add up to seven are considered, including (1, 1, 5), (1, 2, 4), (1, 3, 3), and (2, 3, 2). The key requirement is that these combinations must satisfy the triangle inequality, which states the sum of any two sides must be greater than the third side. After examining each combination, only (1, 3, 3) and (2, 3, 2) satisfy this condition. Thus, there are two possible triangles with the given perimeter.

Keywords

integer sides

triangle inequality

perimeter seven

valid triangles

combinations