The length of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
length of first side+length of second side>length of third side
15+12> 3rd side
3rd >27
To determine the possible range for the length of the third side of the triangle, we need to understand the triangle inequality theorem. According to this theorem, for any triangle, the length of any side must be less than the sum of the lengths of the other two sides.
Let's apply this theorem to the given triangle. We have two sides with lengths 12 cm and 15 cm.
For the third side, let's denote its length as x cm. Applying the triangle inequality theorem, we have the following inequalities:
x < 12 + 15 (since x must be less than the sum of the other two sides)
x < 27
x > 15 - 12 (since x must be greater than the difference of the other two sides)
x > 3
Therefore, the length of the third side should fall between 3 cm and 27 cm.