Question

Which set of side lengths will not create a triangle? responses

a) 2, 5, 8 2, 5, 8, endfragment,
b) 8, 9, 10 8, 9, 10, endfragment,
c) 10, 15, 20 10, 15, 20, endfragment,
d) 10, 14, 18

Answer 1

The set of side lengths that will not create a triangle is option a) 2, 5, 8.

Step-by-step explanation:

A set of side lengths will not create a triangle if the sum of the lengths of any two sides is less than or equal to the length of the third side. Let's analyze the given options:

a) 2, 5, 8: The sum of the two shorter sides (2 + 5) is less than the length of the longest side (8).

b) 8, 9, 10: The sum of the two shorter sides (8 + 9) is greater than the length of the longest side (10). This set of side lengths will create a triangle.

c) 10, 15, 20: The sum of the two shorter sides (10 + 15) is less than the length of the longest side (20).

d) 10, 14, 18: The sum of the two shorter sides (10 + 14) is greater than the length of the longest side (18). This set of side lengths will create a triangle.

Based on the analysis above, the correct answer is option a) 2, 5, 8 because it will not create a triangle.