Question

in triangle abc, ab measures 25 cm and ac measures 35 cm.
the inequality \boxed{} < s < \boxed{} represents the possible third side length of the triangle, s, in centimeters.
the inequality \boxed{} < p < \boxed{} represents the possible values for the perimeter, p, of the triangle, in centimeters.

Explanation:

Step1: Apply triangle inequality to third side

The triangle inequality states that the third side \( s \) must be greater than the absolute difference of the other two sides and less than their sum.
\( |AC - AB| < s < AC + AB \)
\( |35 - 25| < s < 35 + 25 \)
\( 10 < s < 60 \)

Step2: Calculate perimeter bounds

Perimeter \( p = AB + AC + s = 25 + 35 + s = 60 + s \).
Lower bound: \( 60 + 10 = 70 \)
Upper bound: \( 60 + 60 = 120 \)
So \( 70 < p < 120 \)

Answer:

10 < s < 60
70 < p < 120