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 6 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?
The second side is between _____ and _____ inches, and the third side is between ______ and ______ inches.
2007-09-09 13:56:17 · 1 answers · asked by tryshs2001 1 in Science & Mathematics ➔ Mathematics
Let "x" is the lenght of the 3rd side.
Then the lenght of the 2nd side is "2x - 3".
The sum of the lengths of 2nd and 3rd side must be greater then the 1st side:
2x - 3 + x > 6
=> x>3
The 3rd side is greater than 3.
Now what about the 2nd side?
x>3
2x>6
2x-3>3
The 2nd side is also greater than 3.
The sum of the lengths of 1st and 3rd side must be greater then the 2nd side:
6 + x > 2x - 3
=> x<9
The 3rd side is smaller than 9.
x<9
2x<18
2x - 3<15
The 2nd side is smaller than 15.
The answer is:
The second side is between 3 and 15 inches, and the third side is between 3 and 9 inches.
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2007-09-09 15:51:11 · answer #1 · answered by oregfiu 7 · 1⤊ 0⤋