Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point)
Responses
30
15
24
22
You can determine the length of the third side of a triangle using the triangle inequality theorem. According to the theorem, the length of the third side must be greater than the difference between the lengths of the other two sides and less than the sum of the lengths of the other two sides.
In this case, the first two sides measure 10 and 12. Therefore, the length of the third side must be greater than |10-12| (the absolute value of the difference between 10 and 12) and less than 10+12.
Calculating the absolute value of the difference between 10 and 12, we get |10-12| = 2.
Therefore, the length of the third side must be greater than 2 and less than 22 (10+12).
Among the provided choices, only 15 satisfies this condition. So the length of the third side is 15.
So the correct answer is: 15