One side of a triangle measures 14 cm. Another side of the same triangle
measures 6 cm. Which inequalities represent all possible lengths of the
third side, x?
To determine the possible lengths of the third side of the triangle, we can 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.
In this case, let's denote the length of the third side as x. The given lengths of the other two sides are 14 cm and 6 cm.
To find the possible lengths of x, we can form two inequalities:
1. The sum of the two known sides must be greater than the third side: 14 cm + 6 cm > x
Simplifying, we get: 20 cm > x
2. The difference between the two known sides must be less than the third side: 14 cm - 6 cm < x
Simplifying, we get: 8 cm < x
Therefore, the inequalities that represent all possible lengths of the third side, x, are:
8 cm < x < 20 cm