Question

List two sets of possible side lengths for two triangles, one set that forms a triangle and one set that does not.

Answer 1

In any triangle, the sum of lengths of any two sides must be greater than the third side.

(1) If we chose three side lengths to be 5 cm, 7 cm and 10 cm. Let's do the check:
5+ 7 = 12 > 10
5+10 = 15 > 7
7 + 10 = 17 > 5
The sum of any two sides is greater than the third, therefore, these three side lengths can form a triangle.

(2) If we chose three side lengths to be 3 cm, 4 cm and 8 cm.Let's do the check:
3 + 4 = 7 which is not greater than 8
The condition is not fulfilled, therefore, these three side lengths cannot form a triangle.