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 (3 cm, 5 cm, 9 cm)

$3 + 5=8<9$, so it cannot form a triangle.

Step3: Check option 2 (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 (6 cm, 9 cm, 17 cm)

$6+9 = 15<17$, so it cannot form a triangle.

Step5: Check option 4 (8 cm, 10 cm, 18 cm)

$8 + 10=18$, which does not satisfy the triangle - inequality theorem, so it cannot form a triangle.

Answer:

4 cm, 8 cm, 10 cm