Question

Which three lengths cannot be the lengths of the sides of a triangle?

1) 8m, 9m, 10m
2) 7m, 7m, 13m
3) 25m, 16m, 11m
4) 17m, 4m, 10m

Answer 1

The lengths that cannot form the sides of a triangle are options 2) 7m, 7m, 13m and 4) 17m, 4m, 10m, because they violate the Triangle Inequality Theorem.

Step-by-step explanation:

The student is asking which set of three lengths cannot form the sides of a triangle. To determine if three lengths can form a triangle, we use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given this theorem, we analyze the options provided:

• 8m, 9m, and 10m: 8 + 9 > 10, 9 + 10 > 8, and 8 + 10 > 9, so these can form a triangle.
• 7m, 7m, and 13m: 7 + 7 is not greater than 13, so these cannot form a triangle.
• 25m, 16m, and 11m: 25 + 16 > 11, 16 + 11 > 25, and 25 + 11 > 16, so these can form a triangle.
• 17m, 4m, and 10m: 17 + 4 is not greater than 10, so these cannot form a triangle.

Therefore, the sets of lengths that cannot form the sides of a triangle are the options 2) 7m, 7m, 13m and 4) 17m, 4m, 10m.