SOLUTION: 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.

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.
RELATED QUESTIONS
The Lengths of the sides of a triangle are consecutive even integers. Find the length of... (answered by checkley77)

The lengths of the sides of a triangle are consecutive even integers. Find the length of (answered by edjones)

The lengths of the sides of a triangle are consecutive even integers. Find the length of... (answered by MathLover1)

The lengths of the sides of a triangle are consecutive even integers. Find the longest... (answered by ankor@dixie-net.com)

the lengths of the sides of the sides of a triangle are consecutive even integers. find... (answered by solver91311)

The length of the sides of a triangle are consecutive even intergers. Find the length of (answered by checkley77)

The lengths of the sides of a triangle or consecutive even integers. Find the length of... (answered by MathTherapy)

The lengths of the sides of a triangle are three consecutive even integers. Find the... (answered by KMST)

A triangle has a base of lenght 17, and the other two sides are equal in lenght. If the... (answered by Boreal)