Lengths of segmentsTriangleNot a triangle10 m, 14 m, 29 m10 m, 21 m, 29 m10 m, 29 m, 37 m10 m, 29 m, 40 mWhat is a triangle, and what isn’t a triangle?
Accepted Solution
A:
Answer:Triangles: 10 m, 21 m, 29 m10 m, 29 m, 37 mNot triangles:10 m, 14 m, 29 m10 m, 29 m, 40 mStep-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 mThe sum of lengths 10 m and 14 m must be greater than 29 m.10 + 14 = 24 < 29So, this is not a triangle.Option 2: 10 m, 21 m, 29 m10 + 21 = 31 > 2921 + 29 = 50 > 1029 + 10 = 39 > 21Therefore, it is a triangle.Option 3: 10 m, 29 m, 37 m10 + 29 = 39 > 3729 + 37 = 66 > 1037 + 10 = 47 > 29Therefore, it is a triangle.Option 4: 10 m, 29 m, 40 m10 + 29 =39 < 40So, this is not a triangle.