Question

you do: check for understanding 6. a carpenter is searching through scraps of wood to complete the frame of a triangular shadow box. he has two pieces of wood that measure 38.1 centimeters and 40.5 centimeters. what is the range for the measure of the third side?

Explanation:

Step1: Recall triangle inequality rule

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

Step2: Find lower bound of $x$

The third side must be greater than the difference of the two given sides:
$x > 40.5 - 38.1$
$x > 2.4$

Step3: Find upper bound of $x$

The third side must be less than the sum of the two given sides:
$x < 40.5 + 38.1$
$x < 78.6$

Answer:

The measure of the third side must satisfy $2.4$ cm $< x < 78.6$ cm.