If one side of a triangle is 10 inches long, which of the following could NOT be the lengths, in inches, of the other sides?
A. 2 & 9
B. 3 & 5
C. 5& 10
D. 10 & 10
E. 10 & 12
I think it might be B but I don't know and I don't know how to figure the answer.. please help!
B. The length of any side of a triangle must lie in a range between the sum and differnce of the other two sides.
To determine which of the listed pairs of lengths could not be the lengths of the other two sides of the triangle, we can utilize the Triangle Inequality Theorem.
According to the Triangle Inequality Theorem, in a triangle, the sum of the lengths of any two sides must always be greater than the length of the remaining side.
Let's evaluate each option:
A. 2 & 9: The sum of the two sides (2 + 9 = 11) is greater than the remaining side (10). So, this pair satisfies the Triangle Inequality Theorem.
B. 3 & 5: The sum of the two sides (3 + 5 = 8) is less than the remaining side (10). So, this pair does not satisfy the Triangle Inequality Theorem.
C. 5 & 10: The sum of the two sides (5 + 10 = 15) is greater than the remaining side (10). So, this pair satisfies the Triangle Inequality Theorem.
D. 10 & 10: The sum of the two sides (10 + 10 = 20) is greater than the remaining side (10). So, this pair satisfies the Triangle Inequality Theorem.
E. 10 & 12: The sum of the two sides (10 + 12 = 22) is greater than the remaining side (10). So, this pair satisfies the Triangle Inequality Theorem.
Based on the Triangle Inequality Theorem, the only pair that does not fulfill the criteria is option B (3 & 5). Therefore, option B is the answer.
To solve this question, you need to know the Triangle Inequality Theorem and how to apply it.