Question

Applying the Triangle Inequality Theorem in triangle ABC, AB measures 25 cm and AC measures 35 cm.

The possible third side length of the triangle is between:
A) 10 and 60 centimeters
B) 10 and 70 centimeters
C) 10 and 80 centimeters
D) 10 and 90 centimeters

Answer 1

The possible third side length of the triangle is between 10 and 60 centimeters.

Step-by-step explanation:

The Triangle Inequality Theorem states that, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In triangle ABC, AB measures 25 cm and AC measures 35 cm.

To find the possible range of the length of the third side, we can apply the Triangle Inequality Theorem. Considering AB and AC as the two sides, the third side must satisfy the inequality:

AB + AC > BC
25 + 35 > BC
60 > BC
So, the possible third side length of the triangle is between 10 and 60 centimeters. Therefore, the correct option is A) 10 and 60 centimeters.