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
24
24
15
15
22
22
30
To determine the length of the third side of a triangle, you can use the triangle inequality theorem. According to this theorem, 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 first two sides measure 10 and 12. So, let's check the choices provided using the triangle inequality theorem:
1. The sum of the first and second sides (10 + 12 = 22) is greater than 24. This means that a triangle with side lengths 10, 12, and 24 is possible.
2. The sum of the first and second sides (10 + 12 = 22) is greater than 15. This means that a triangle with side lengths 10, 12, and 15 is possible.
3. The sum of the first and second sides (10 + 12 = 22) is less than 22. This means that a triangle with side lengths 10, 12, and 22 is not possible.
4. The sum of the first and second sides (10 + 12 = 22) is less than 30. This means that a triangle with side lengths 10, 12, and 30 is not possible.
Therefore, the only valid option is 15. The length of the third side of the triangle is 15.