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

Algebra ->  Expressions-with-variables -> SOLUTION: The lengths of the sides of a triangle are three consecutive even integers. Find the length of the longest side if it is 22 units shorter than the perimeter. Thank you.      Log On


   

Question 812756: The lengths of the sides of a triangle are three consecutive even integers. Find the length of the longest side if it is 22 units shorter than the perimeter.
Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x=perimeter-22= length of the longer side,
so x%2B22=perimeter

Since consecutive even integers are 2 units apart,
x-2= length of the medium-length side
x-4= length of the shortest side

The perimeter is the sum of the side lengths, so
x%2B%28x-2%29%2B%28x-4%29=x%2B22
That is our equation.
I will work on that equation in lots of baby steps,
just in case you want to see all those steps.
You probably want to use less steps,
and your teacher probably does not expect or want to see too many steps.

x%2B%28x-2%29%2B%28x-4%29=x%2B22
x%2Bx-2%2Bx-4=x%2B22
x%2Bx%2Bx-2-4=x%2B22
Adding 6 to both sides of the equal sign, we get
x%2Bx%2Bx-2-4%2B6=x%2B22%2B6
x%2Bx%2Bx%2B6-2-4=x%2B28
%28x%2Bx%2Bx%29%2B%286-2-4%29=x%2B28
3x%2B0=x%2B28
3x=x%2B28
3x-x=x%2B28-x
3x-x=28%2Bx-x
2x=28%2B%28x-x%29
2x=28
2x%2F2=28%2F2
highlight%28x=14%29