Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.(1 point)
Responses
5 mm
5 mm
2 mm
2 mm
20 mm
20 mm
1 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 lengths of the two given sides are 10 mm and 7 mm. Therefore, the third side must have a length less than the sum of these two sides, but greater than the difference between these two sides.
Sum of the two given sides: 10 mm + 7 mm = 17 mm
Difference between the two given sides: 10 mm - 7 mm = 3 mm
Therefore, the length of the third side must be greater than 3 mm but less than 17 mm.
From the choices given:
- 5 mm is within this range
- 2 mm is less than 3 mm, so it is not a possible length for the third side
- 20 mm is greater than 17 mm, so it is not a possible length for the third side
- 1 mm is less than 3 mm, so it is not a possible length for the third side
Therefore, the length of the third side is most likely 5 mm.