Question

use the image to answer the question. determine which value is possible for x. (1 point)

Explanation:

Step1: Apply 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. So, we have two inequalities: $x + 17>21$ and $x+21 > 17$ and $17 + 21>x$.

Step2: Solve the first inequality

For $x + 17>21$, subtract 17 from both sides: $x>21 - 17$, so $x>4$.

Step3: Consider the third - inequality

For $17 + 21>x$, we have $x<38$.

Answer:

$4 < x<38$