Atriangle has two side of length 10 and 14 what value could the length of the third side be check all that apply a) 26b) 16c) 10d) 8e) 5f) 2

To solve such problems we need to know about the triangle inequality theorem.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than or equal to the third side.

A triangle has two sides of length 10 and 14.

As given two sides, therefore,

a = 10,

b = 14,

(a+b) ≥ c,

(10+14) ≥ c,

(24) ≥ c,

Therefore, any side less than or equal to 24 can be the third side of the triangle,

A) 26,

26 is greater than 24. thus, A can not be the third side of the triangle.

B) 16

16 is less than 24. thus, B can be the third side of the triangle.

C) 10

10 is less than 24. thus, C can be the third side of the triangle.

D) 8

8 is less than 24. thus, D can be the third side of the triangle.

E) 5

5 is less than 24. thus, E can be the third side of the triangle.

F) 2

2 is less than 24. but, the sum of 10 and 2 will not be greater than the third side which is 14. thus, F can not be the correct option.

Learn more about triangle inequality theorem:

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If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A) 10, 14, 26

10 + 14 = 24 < 26   INCORRECT  :(

B) 10, 14, 16

10 + 14 = 24 > 16  CORRECT :)

C) 10, 10, 14

10 + 10 = 20 > 14  CORRECT :)

D) 8, 10, 14

8 + 10 = 18 > 14   CORRECT :)

E) 5, 10, 14

5 + 10 = 15 > 14   CORRECT :)

F) 2, 10, 14

2 + 10 = 12 < 14   INCORRECT :(