Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.
2 mm 20 mm 1 mm 5 mm
To determine the length of the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides are 10 mm and 7 mm. Let's consider each choice:
1) 2 mm: 10 + 2 = 12, which is greater than 7. However, 7 + 2 = 9, which is not greater than 10. So, 2 mm is not a valid length for the third side.
2) 20 mm: 10 + 20 = 30, which is greater than 7. However, 7 + 20 = 27, which is not greater than 10. So, 20 mm is not a valid length for the third side.
3) 1 mm: 10 + 1 = 11, which is greater than 7. However, 7 + 1 = 8, which is not greater than 10. So, 1 mm is not a valid length for the third side.
4) 5 mm: 10 + 5 = 15, which is greater than 7. Also, 7 + 5 = 12, which is greater than 10.
Therefore, the length of the third side of the triangle is 5 mm.