Question

describe the possible lengths for the third side of a triangle with two sides of 6 in and 9 in using a compound inequality. (hint: use < or > to submit your answer.)

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side. Let the sides of the triangle be $a = 6$, $b = 9$, and the third - side be $x$.

Step2: Calculate the lower bound

$|a - b|

Step3: Calculate the upper bound

$xCombining these two inequalities gives $3 < x < 15$.

Answer:

$3 < x < 15$