Question

A triangle has two side lengths 7 and 9. What value could the length of the third side be? Check all that apply

A. 8
B. 5
C. 10
D. 2
E. 13
F. 22

Answer 1

Each side has to be less then the sum of the other two sides.
A, B, C, and E work.

Answer 2

`8,5,10,13`

Explanation:

Let

x-----> the length of the third side

we know that

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side

so

case A)

`7+9 >x\\16> x\\x<16\ units`

case B)

`7+x >9\\x>9-7\\ x>2\ units`

The solution for the length of the third side is the interval------>
`(2,16)`

All real numbers greater than
`2` and less than
`16`

therefore

the solutions are

`8,5,10,13`