two sides of a triangle are 10 mm and 7 mm. using the triangle inequality theorem determine the length of the third side from choices given
To determine the possible range of lengths for the third side of the triangle, we need to apply 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 call the third side length x mm. According to the Triangle Inequality Theorem, we have two inequalities:
1. x + 10 > 7 (since 7 mm + 10 mm > x mm)
2. 7 + x > 10 (since 7 mm + x mm > 10 mm)
We can solve these inequalities to find the possible range of lengths for the third side (x):
1. x > -3 (subtracting 10 from both sides)
2. x > 3 (subtracting 7 from both sides)
Therefore, the third side (x) must have a length greater than 3 mm.