Question

Question 3 of 10

A triangle has two sides of lengths 10 and 14. What value could the length of
the third side be? Check all that apply.
A. 26
B. 5
C. 2
D. 8
E 16
F. 10

Answer 1

Options B, C, D and E are correct answers.

Given that, a triangle has two sides of lengths 10 and 14.

We need to find what value could the length of the third side be and check all that apply.

What is the triangle inequality theorem?

Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

Now, from the given options:

A) 10, 14, 26

10 + 14 = 24 < 26 the triangle can not be formed

B) 10, 14, 16

10 + 14 = 24 > 16 the triangle can be formed

C) 10, 10, 14

10 + 10 = 20 > 14 the triangle can be formed

D) 8, 10, 14

8 + 10 = 18 > 14 the triangle can be formed

E) 5, 10, 14

5 + 10 = 15 > 14 the triangle can be formed

F) 2, 10, 14

2 + 10 = 12 < 14 the triangle can not be formed

Therefore, options B, C, D and E are correct answers.

Answer 2

By the Triangle Inequality Theorem:

10 + 14 > x, so x < 24

10 + x > 14, so x > 4

We have 4 < x < 24, so B, D, E, and F are correct.