Question

two sides of a triangle have lengths 42 inches and 16 inches. which inequality shows all possible values for the measure of the third side, x, in inches? a. 0 < x < 16 b. 0 < x < 26 c. 16 < x < 42 d. 26 < x < 42 e. 26 < x < 58

Explanation:

Step1: Find lower bound of x

The third side must be greater than the difference of the two given sides.
$x > 42 - 16$
$x > 26$

Step2: Find upper bound of x

The third side must be less than the sum of the two given sides.
$x < 42 + 16$
$x < 58$

Step3: Combine inequalities

Combine the lower and upper bounds to get the range for x.
$26 < x < 58$

Answer:

E. $26 < x < 58$