Question

1. gerald and jessie are deciding which measure to use for the third side of a triangular logo for their company. if the measures of two sides are 25 inches and 52 inches, which inequality describes all their possible choices for the third side?

a. 25 < x < 52
b. 27 > x > 77
c. 27 < x < 77
d. 25 > x > 52

Explanation:

Step1: Recall triangle inequality rule

For a triangle with sides $a$, $b$, $x$, $|a-b| < x < a+b$

Step2: Calculate lower bound

Subtract the two sides: $52 - 25 = 27$

Step3: Calculate upper bound

Add the two sides: $52 + 25 = 77$

Step4: Form the inequality

Combine bounds: $27 < x < 77$

Answer:

C. $27 < x < 77$