Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.
A. 24
B. 30
C. 15
D. 22
To find the length of the third side of a triangle using the given side lengths, we can use the triangle inequality theorem. According to the theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Given that the first two sides measure 10 and 12, let's check the possible choice options:
A. 24: 10 + 12 = 22, which is less than 24. Therefore, this option does not satisfy the triangle inequality theorem.
B. 30: 10 + 12 = 22, which is less than 30. Therefore, this option does not satisfy the triangle inequality theorem.
C. 15: 10 + 12 = 22, which is greater than 15. Therefore, this option satisfies the triangle inequality theorem.
D. 22: 10 + 12 = 22, which is equal to 22. Therefore, this option does not satisfy the triangle inequality theorem.
Based on the triangle inequality theorem, the correct answer is C. 15.