Two sides of a triangle measure 3.7 and 8.2. Apply the Triangle Inequality Theorem to find a possible measure of the third side
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let x be the length of the third side.
Therefore, we have the following inequalities:
3.7 + 8.2 > x
x + 3.7 > 8.2
x + 8.2 > 3.7
Solving the inequalities:
3.7 + 8.2 > x
12.9 > x
x + 3.7 > 8.2
x > 4.5
x + 8.2 > 3.7
x > -4.5
Since the lengths of the sides must be positive, the possible measure of the third side, x, is between 4.5 and 12.9.