SOLUTION: 17. A triangle has a perimeter of 27 feet. One side is 8 feet. The middle side is five less than the longest side. What are the lengths of the middle and longest side?

Question 415824: 17. A triangle has a perimeter of 27 feet. One side is 8 feet. The middle side is five less than the longest side. What are the lengths of the middle and longest side?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
(1) S+M+L=27, where S=shortest side, M=middle side, L=longest side
(2) M=L-5
We are told that one of the sides is 8 feet. We know this cannot be the longest side, since the middle side would be 5 less than this, or 3 feet. This combination would give a perimeter < 27 feet. It also cannot be the shortest side, since the middle side would have to be at least 9 and the longest side is 5 more than that, or 14. This perimeter is > 27 feet. Therefore the length of the middle side is 8 feet.
From (2), L=M+5 -> L = 13 feet.
Using (1), S=27-13-8 = 6 feet.
Answer: S=6,M=8,L=13
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