Two sides of a triangle are 10 mm and 7 mm. Using the Triangle Inequality Theorem, determine the length of the third side from the choices given. (1 point) Responses 5 mm 2 mm 1 mm 20 mm
Using the Triangle Inequality Theorem, the length of the third side of the triangle must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
To find the possible range of the length of the third side, we can use the inequality:
7 mm - 10 mm < x < 7 mm + 10 mm
Simplifying this inequality, we get:
-3 mm < x < 17 mm
Therefore, the length of the third side must be greater than -3 mm and less than 17 mm.
None of the given choices (5 mm, 2 mm, 1 mm, 20 mm) fall within this range, so there is no answer from the choices given.