Question

a triangle has two sides of length 7 and 9. what is the smallest possible whole - number length for the third side?

Explanation:

Step1: Recall triangle inequality theorem

For a triangle with sides $a, b, c$, the sum of any two sides must be greater than the third side. Let the third side be $x$.

Step2: Set up inequalities

We have three inequalities:
$7 + 9 > x$ → $16 > x$
$7 + x > 9$ → $x > 9 - 7$
$9 + x > 7$ → $x > 7 - 9$ (this is always true since length is positive)

Step3: Simplify valid inequality

Focus on $x > 9 - 7$ → $x > 2$

Step4: Find smallest whole number

The smallest whole number greater than 2 is 3.

Answer:

3