Question

A triangle has two sides of lengths 8 and 10.what value could the length of the third side be? Check all that apply..

A:10
B:8
C:7
D:4
E:20
F:18

Answer 1

A: 10

B: 8

C: 7

D: 4

Explanation:

Answer 2

Option A, B , C and D are correct.

Explanation:

By triangle inequality theorem:

This theorem states that the sum of any two sides of a triangle must be greater than the third side.

As per the statement:

A triangle has two sides of lengths 8 and 10.

Let third side be x.

Sum of the two sides is:

8 + 10 = 18

By triangle inequality theorem:

18 > x

or

x < 18

⇒ the length of third side must be less than 18

From the given options:

Length of third sides 4, 7, 8, 10 which are less than 18

Therefore, the value which could the length of the third side be are: 4, 7, 8, 10