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

Algebra ->  Inequalities -> 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      Log On


   

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(39838) About Me  (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.

2x-3%2Bx%3E18, picking the side #2 and side #3 to compare to side #1.
3x-3%3E18
3x%3E21
x%3E7
highlight%28x%3E7%29

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.

18%2Bx%3E2x-3
18%2B3%3Ex
21%3Ex

Do one more just to be certain.
18%2B2x-3%3Ex
18%2Bx-3%3E0
x%3E-15, which is not very meaningful.

The intersection of all three solutions is highlight%28x%3E21%29.

Side number 2 would be 2x-3 for x>21,
2%2A21-3, which is 39 at its limit.