Question

if two sides of a triangle have lengths 4 and 9, then the length of the third side may be any number
less than 13
greater than 4 but less than 9
greater than 5 but less than 13
greater than 5

Explanation:

Step1: Recall triangle inequality theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side, and the difference of the lengths of any two sides must be less than the length of the remaining side.

Step2: Apply the theorem to the given sides

Let the length of the third side be \( x \). Given two sides are 4 and 9.
First, the sum of the two sides: \( 4 + 9>x \), so \( x < 13 \).
Second, the difference of the two sides: \( 9 - 45 \).

Answer:

greater than 5 but less than 13