To find the range for the measure 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.
Let's consider the two given sides: 6 and 7.
For the third side to be able to form a triangle, the sum of the lengths of the other two sides must be greater than the length of the third side.
So we have two cases to consider:
1) If we add 6 and 7 together: 6 + 7 = 13. In this case, the third side must be greater than 13 for a triangle to be formed.
2) If we subtract 6 from 7: 7 - 6 = 1. In this case, the third side must be less than 1 for a triangle to be formed. However, since a side length cannot be negative, we can ignore this case.
Therefore, the range for the measure of the third side of the triangle is all values greater than 13.
Find the range for the measure of the third side of the triangle when the measure of two sides is 6 and 7
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