Question 420018: The perimeter of any triangle is the sum of the lengths of its sides. The lengths of the sides of a certain triangle, in feet, are consecutive even integers. The perimeter of this triangle is between 10ft and 24ft inclusive. How do I write an inequality to describe the possible measures of the perimeter of the triangle?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let a, b, and c be the lengths of the sides of the triangle. So the perimeter is a+b+c. Because we know that the perimeter is between 10 and 24 (inclusive), we know that
Moreover, we know that the three sides are consecutive integers. So a=x, b=x+1, and c=x+2 for some integer x. So replace a, b, and c to get
 Combine like terms
 Subtract 5 from all sides
 Combine like terms.
 Divide all sides by 3 to isolate x
 Divide 5 by 3 to get 2.6667 and round down to get 2. Since 2.667 is larger than 2 and x > 2.667, this means that x > 2.
 Divide 21 by 3 to get 7
So the possible values for a range from 2 (non inclusive) to 7 (inclusive). So the values of a are: 3, 4, 5, 6, 7
Note: the values of b and c depend on a.
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Jim
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