SOLUTION: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18 inches and a second side that is 3 inches less than
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Question 917636: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18 inches and a second side that is 3 inches less than twice the third side, what are the possible lengths for the second and third sides?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Description of the sides of your triangle:
18; and -3+2x; and x.
According to the THEOREM you quoted, picking any two sides should conform to the theorem as stated.
, picking the side #2 and side #3 to compare to side #1.
Now you also need to examine comparing sum of sides 1 and 3 with length of side 2, using the triangle inequality theorem. THEN take the values for x which satisfy BOTH inequalities.
Do one more just to be certain.
, which is not very meaningful.
The intersection of all three solutions is .
Side number 2 would be 2x-3 for x>21,
, which is 39 at its limit.
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