Lengths of segments

Triangle

Not a triangle

10 m, 14 m, 29 m

10 m, 21 m, 29 m

10 m, 29 m, 37 m

10 m, 29 m, 40 m

What is a triangle, and what isn't a triangle?

Triangles:

10 m, 21 m, 29 m

10 m, 29 m, 37 m

Not triangles:

10 m, 14 m, 29 m

10 m, 29 m, 40 m

Step-by-step explanation:

For a triangle to exist, the sum of any two sides of a triangle must be greater than that of the third side.

Let us check each of the options.

Option 1: 10 m, 14 m, 29 m

The sum of lengths 10 m and 14 m must be greater than 29 m.

10 + 14 = 24 < 29

So, this is not a triangle.

Option 2: 10 m, 21 m, 29 m

10 + 21 = 31 > 29

21 + 29 = 50 > 10

29 + 10 = 39 > 21

Therefore, it is a triangle.

Option 3: 10 m, 29 m, 37 m

10 + 29 = 39 > 37

29 + 37 = 66 > 10

37 + 10 = 47 > 29

Therefore, it is a triangle.

Option 4: 10 m, 29 m, 40 m

10 + 29 = 39 < 40

So, this is not a triangle.