Calculating the length of the third side of a triangle

To calculate the length of the third side of a triangle, we need to use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Using the triangle inequality theorem

Let's apply this theorem to the given problem. We know that the length of two sides of the triangle is 8 cm and 12 cm. Let's call the length of the third side x.

According to the triangle inequality theorem, we have:

8 + 12 > x

Simplifying, we get:

20 > x

This means that the length of the third side must be less than 20 cm for the triangle to be valid.

Determining the possible lengths of the third side

To determine the possible lengths of the third side, we need to consider the range of values that x can take. Since x must be less than 20 cm, we can write:

0 < x="" />< 20="" />

This means that the length of the third side can be any value between 0 cm and 20 cm (excluding 0 and 20 cm).

Conclusion

In conclusion, the length of the third side of the triangle can be any value between 0 cm and 20 cm, excluding 0 and 20 cm. To determine the exact length of the third side, we would need more information about the triangle, such as the angles or the type of triangle.

It will be difference than the sum of 8 & 12 cm & smaller than the sum of 8 & 12