Question 174025: The lenght of the sides of a triangle are consecutive even integers. Find the lenght of the longest side if it is 22 units shorter that the perimeter.
Answer by SAT Math Tutor(36)   (Show Source):
You can put this solution on YOUR website! Ok, well if all the sides are consecutive even integers they can be written as follows:
2n
2n + 2
2n + 4
So, the perimeter is 2n + (2n + 2) + (2n + 4) or 6n + 6
Since the longest side is 2n + 4 and it is 22 units shorter than the perimeter we have,
(2n + 4) + 22 = 6n + 6
2n + 26 = 6n + 6
2n = 6n - 20
-4n = -20
n = 5
The longest side is 2n + 4 and n = 5 so 2(5) + 4 = 14 is the longest side.
Thus, the triangle has sides, 10, 12, 14.
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