Question

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

Answer 1

Answer:

$8,5,10,13$

Step-by-step 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)

$7+9 >x\\16> x\\x$

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

$8,5,10,13$

Answer 2

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