To determine the possible side measures that can be used to create a triangle using the given lengths (97 and 56), we apply the triangle inequality theorem. The possible side measures for the third side length, c, are greater than -41 and less than 41.
To determine the possible side measures that can be used to create a triangle using the given lengths, we need to apply the triangle inequality theorem. According to the 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 denote the given side lengths as a = 97 and b = 56. To find the possible side measures, we will evaluate the following inequalities:
a + b > c, where c is the third side length
a + c > b
b + c > a
Substituting the given values, we obtain:
97 + 56 > c → 153 > c
97 + c > 56 → c > -41
56 + c > 97 → c > 41
Therefore, the possible side measures for the third side length, c, are greater than -41 and less than 41.