Which three length cannot be the length of the sides of a triangle

The missing choices are here

A. 23 m, 17 m, 14 m

B. 11 m, 11 m, 12 m

C. 5 m, 7 m, 8 m

D. 21 m, 6 m, 10 m

Answer:

21 m, 6 m, 10 m cannot be the length of the sides of a triangle ⇒ D

Step-by-step explanation:

There is a fact to form a triangle:

The sum of the lengths of the two smaller sides must be greater than the length of the third side

A.

∵ The smallest sides are 14 m and 17 m

∵ Their sum = 14 + 17 = 31 m

∵ The third side is 23 m

∵ 31 > 23

∴ 23 m, 17 m, 14 m can be the length of the sides of a triangle

B.

∵ The smallest sides are 11 m and 11 m

∵ Their sum = 11 + 11 = 22 m

∵ The third side is 12 m

∵ 22 > 12

∴ 11 m, 11 m, 12 m can be the length of the sides of a triangle

C.

∵ The smallest sides are 5 m and 7 m

∵ Their sum = 5 + 7 = 12 m

∵ The third side is 8 m

∵ 12 > 8

∴ 5 m, 7 m, 8 m can be the length of the sides of a triangle

D.

∵ The smallest sides are 6 m and 10 m

∵ Their sum = 6 + 10 = 16 m

∵ The third side is 21 m

∵ 16 < 21

∴ 21 m, 6 m, 10 m cannot be the length of the sides of a triangle