SOLUTION: A triangle has a perimeter of 30. If the longest side is 2 less than 3 times the shortest side and the medium side is 2 more than twice the shortest side, then how long is each sid

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Question 595663: A triangle has a perimeter of 30. If the longest side is 2 less than 3 times the shortest side and the medium side is 2 more than twice the shortest side, then how long is each side of the triangle?
Answer by math-vortex(648) About Me  (Show Source):
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A triangle has a perimeter of 30. If the longest side is 2 less than 3 times the shortest side and the medium side is 2 more than twice the shortest side, then how long is each side of the triangle?
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Hi. there--
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We have the perimeter (the distance around the edge) of the triangle. We need to translate the English description of each side length into an algebraic expression. Then we can write an equation and solve for each side length.
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Notice that each description is written in terms of the shortest side. Let's call that side s.
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Now for the longest side. We translate the "2 less than 3 times the shortest side" as 3s-2.
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Next, we find an expression for the medium side. We translate "2 more than twice the shortest side" as 2s+2.
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We know that the perimeter is 30, so the three sides must add to 30. We write that as an equation.
s%2B%283s-2%29%2B%282s%2B2%29=30
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Simplify this equation by combining like terms. Then solve for s.
s%2B%283s-2%29%2B%282s%2B2%29=30
6s=30
s=5
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Now substitute 5 for s each expression to find the lengths of each side.
longest side: 3s-2=3(5)-2=13
medium side: 2s+2=2(5)+2=12
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The final step is to check our work against the original wording of the problem.
"A triangle has a perimeter of 30": 5+13+12=30 YES!
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"the longest side is 2 less than 3 times the shortest side": "13 is 2 less than 3 time 5," or "13 is 2 less than 15." YES!
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"the medium side is 2 more than twice the shortest side": "12 is 2 more than twice 5," or "12 is 2 more than 10." YES!
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That's it! I hope this helps! Feel free to email if any part of the explanation in unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com