Question

which are the possible side lengths of a triangle?
4 cm, 8 cm, 10 cm
6 cm, 9 cm, 17 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 4 cm, 8 cm, 10 cm:
$4 + 8=12>10$, $4 + 10 = 14>8$, $8+10 = 18>4$.

Step3: Check option 2

For side lengths 6 cm, 9 cm, 17 cm:
$6 + 9=15<17$.

Answer:

4 cm, 8 cm, 10 cm