Two sides of a triangle measure 9 cm and 23 cm. Which could be the measure of the third side of the triangle?
The third side x must satisfy 23-9 < x < 23+9
To find the possible measures of the third side of the triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider the given side lengths:
- Side A: 9 cm
- Side B: 23 cm
Applying the Triangle Inequality Theorem, we can write two inequalities:
1) Side A + Side B > Third side
9 cm + 23 cm > Third side
32 cm > Third side
2) Side B + Third side > Side A
23 cm + Third side > 9 cm
Third side > -14 cm (This is not possible, as length cannot be negative)
So, combining the inequalities, we can see that the third side must be greater than 9 cm and less than 32 cm.
Therefore, the possible measures for the third side of the triangle are any values greater than 9 cm and less than 32 cm.