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 :(
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:
https://brainly.com/question/309896
