Question

Which set of measurements can represent the lengths of a triangle's sides?

Classify each set of lengths as a Triangle or Not a triangle.

Lengths of segments Triangle Not a triangle
10 m, 14 m, 29 m


10 m, 21 m, 29 m


10 m, 29 m, 40 m


10 m, 29 m, 37 m

Answer 1

Use the triangle inequality: the sum of any two side lengths must be greater than the third.

- 10 m, 14 m, 29 m — Not a triangle (10 + 14 = 24 ≤ 29)
- 10 m, 21 m, 29 m — Triangle (10 + 21 = 31 > 29)
- 10 m, 29 m, 40 m — Not a triangle (10 + 29 = 39 ≤ 40)
- 10 m, 29 m, 37 m — Triangle (10 + 29 = 39 > 37)