two sides of a triangle are 10 mm and 7 mm. determine the length of the third side from the choices given.

20 mm
1 mm
2 mm
5 mm

1 answer

To determine the length of the third side of the 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.

Given that two sides are 10 mm and 7 mm, the third side must be less than the sum of these two sides and greater than their difference.

10 + 7 > x
17 > x

10 - 7 < x
3 < x

Therefore, the length of the third side must be greater than 3 mm and less than 17 mm.

From the choices given, the only length that falls within this range is 5 mm. Therefore, the length of the third side is 5 mm.