Triangle ABC has two sides, length 5 cm and 8 cm. Give three possible lengths for the third side.

1 answer

Let x be the length of the third side.

1) When x is 3 cm, triangle ABC is a degenerate triangle with all vertices lying on the same line, making the total length of all sides 5 cm.

2) When x is 13 cm, triangle ABC is a triangle where the third side is the longest side, but it is still possible for the triangle to be formed.

3) When x is 1 cm, the third side is shorter than the difference between the lengths of the other two sides, making it impossible to form a triangle.