Question

which are the possible side lengths of a triangle? 3 cm, 5 cm, 9 cm 4 cm, 8 cm, 10 cm 6 cm, 9 cm, 17 cm 8 cm, 10 cm, 18 cm

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check option 1

For side - lengths 3 cm, 5 cm, 9 cm: $3 + 5=8<9$, so it cannot form a triangle.

Step3: Check option 2

For side - lengths 4 cm, 8 cm, 10 cm:
$4 + 8 = 12>10$;
$4+10 = 14>8$;
$8 + 10=18>4$. So it can form a triangle.

Step4: Check option 3

For side - lengths 6 cm, 9 cm, 17 cm: $6 + 9=15<17$, so it cannot form a triangle.

Step5: Check option 4

For side - lengths 8 cm, 10 cm, 18 cm: $8 + 10 = 18$, which does not satisfy the triangle - inequality theorem (the sum must be strictly greater), so it cannot form a triangle.

Answer:

4 cm, 8 cm, 10 cm