Question

In triangle ABC, AB measures 25 cm and AC measures 35 cm.



The inequality
< s <
represents the possible third side length of the triangle, s, in centimeters.



The inequality
< p <
represents the possible values for the perimeter, p, of the triangle, in centimeters.

Answer 1

By the triangle inequality, |35 − 25| < s < 35 + 25, so 10 < s < 60.

Perimeter p = 25 + 35 + s = 60 + s, so 60 + 10 < p < 60 + 60, hence 70 < p < 120.