Which of the following are the possible lengths to complete a triangle with side lengths of 14 in. and 8 in.?
greater than 6 in., less than 20 in
greater than 6 in., less than 22 in.
greater than 4 in., less than 20 in.
greater than 4 in., less than 22 in.
Which of the following are the possible lengths to complete a triangle with side lengths of 14 in. and 8 in.?
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To determine the possible lengths of the third side of a triangle when two side lengths are given (14 in. and 8 in.), we use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let ( c ) be the length of the third side. According to the triangle inequality, we have:
1. ( 14 + 8 > c ) → ( c < 22 ) 2. ( 14 + c > 8 ) → ( c > -6 ) (which is always true since lengths are positive)
3. ( 8 + c > 14 ) → ( c > 6 )
Combining the relevant inequalities, we find:
– ( c > 6 )
– ( c < 22 )
Thus, the possible lengths for the third side are: greater than 6 in. and less than 22 in.
So, the correct answer is greater than 6 in., less than 22 in.