Question

Which group of side lengths will NOT create a triangle? 7, 6, 10 4, 2, 7 3, 4, 5 3, 3,3

Answer 1

Triangle inequality

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side.

Let's analyze each group of side lengths:

• 7,6,10

Note that:

7+6 > 10

7+10 > 6

6+10 > 7

Since all the conditions are met, this group can create a triangle

• Now for 4,2,7

Testing each sum:

4+2 > 7

This inequality is false since 6 is not greater than 7

Thus, this group cannot create a triangle

• Now for 3,4,5

Testing each sum:

3 + 4 > 5

3 + 5 > 4

4 + 5 > 3

Since all the conditions are met, this group can create a triangle

• Finally, for 3,3,3

Testing each sum:

3 + 3 > 3

This happens three times. They form in fact an equilateral triangle

Thus, the only group that cannot create a triangle is 4,2,7