The measures of two sides of a triangle are 9 and 15. Use an inequality to express the range of the measure of the third side,m.
To express the range of the measure of the third side, m, we can use the triangle inequality theorem. According to the theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
So, in this case, let's consider the two sides with measures 9 and 15. We can express the range of the measure of the third side, m, using the following inequality:
9 + 15 > m
This inequality states that the sum of the measures of the two known sides, 9 and 15, must be greater than the measure of the third side, m. This follows the triangle inequality theorem.
Simplifying the inequality, we have:
24 > m
Therefore, the range of the measure of the third side, m, is any value less than 24.