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

- 4 cm, 8 cm, 10 cm are the possible side lengths of a triangle.

Explanation:-

We know that in a triangle the sum of any two sides of a triangle must be greater than the third side.

Given :

1. Measurement of first triangle=3 cm, 5 cm, 9 cm

Now, for triangle Sum of two sides > third side

⇒3+5>9

⇒8>9 , which is not true.

∴ Triangle with these side lengths is not possible.

2.Measurement of second triangle=4 cm, 8 cm, 10 cm

Now, for triangle Sum of two sides > third side

⇒4+8>10⇒12>10, which is true.

⇒8+10>4⇒18>4, which is true.

⇒4+10>8⇒14>8, which is true.

∴Triangle with these side lengths is possible.

3. Measurement of third triangle=6 cm, 9 cm, 17 cm

Now, for triangle Sum of two sides > third side

⇒6+9>17⇒17>17 , which is not true.

∴Triangle with these side lengths is not possible.

4. Measurement of fourth triangle=8 cm, 10 cm, 18 cm

Now, for triangle Sum of two sides > third side

⇒8+10>18⇒18>18 , which is not true.

∴Triangle with these side lengths is not possible.

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