SOLUTION: the lengths of the sides of the sides of a triangle are consecutive even integers. find the length of the longest side if it is 22 units shorter than the perimeter.

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Question 174026: the lengths of the sides of the sides of a triangle are consecutive even integers. find the length of the longest side if it is 22 units shorter than the perimeter.
Answer by solver91311(24713) About Me  (Show Source):
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Three consecutive even integers are: x, x%2B2, and x%2B4.

Their sum, x%2Bx%2B2%2Bx%2B4=3x%2B6 is the perimeter.

The longest side, x%2B4 is 22 units shorter than the perimeter, so x%2B4%2B22=x%2B26 is the perimeter.

Having two expressions for the perimeter, we can set them equal:

3x%2B6=x%2B26

3x-x=26-6

2x=20

x=10

So the sides are 10, 12, and 14. The perimeter is then 10+%2B+12+%2B+14+=+36 and 36-22=14 so the answer checks.