Using the Triangle Inequality Theorem (see picture above), determine the length of the third side of the triangle.

Answer 1

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the lengths of the two sides given are 5 cm and 8 cm.

So, we need to check if the sum of these two sides is greater than the length of the third side:
5 cm + 8 cm = 13 cm

Since 13 cm is greater than the length of the third side, the triangle is possible.

Therefore, the length of the third side can be any value between 5 cm and 8 cm.