The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, to choose the set of numbers that cannot be the measures of the sides of a triangle, we will check if the sum of two smallest numbers is greater than the greatest number for each of the given sets.
Given set of numbers
Triangle Inequality
Simplify
10, 11, 20
10+ 11? > 20
21>20 âś“
14, 16, 28
14+ 16? > 28
30>28 âś“
35, 45, 75
35+ 45? > 75
80>75 âś“
41, 55, 98
41+ 55? > 98
96≯ 98 *
As we can see, in the last set the sum of two smallest numbers is not greater than the greatest number. Therefore, the last set of numbers cannot be the measures of the sides of a triangle. This corresponds with answer D.
