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)
A. 5 mm
B. 2 mm
C. 1 mm
D. 20 mm
According to the Triangle Inequality Theorem, the length of the third side of a 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.
In this case, the lengths of the two sides are 10 mm and 7 mm.
For the third side to be a valid length, it must be greater than the difference between the lengths of the other two sides:
10 mm - 7 mm = 3 mm
The third side must also be less than the sum of the lengths of the other two sides:
10 mm + 7 mm = 17 mm
Therefore, the valid length of the third side falls between 3 mm and 17 mm.
The only option that falls within this range is:
D. 20 mm
So, the length of the third side is 20 mm.