Fractional equations

Question

The lengths of the sides of a triangle are consecutive even integers. One fifth of the perimeter is 6 less than the length of the shortest side. Find the perimeter. 

Answer 1

This is a fun problem. The first statement tells us that:

 

s + (s+2) +(s +4) = P

3s + 6 = P

 

The next statement is a little more confusing, but it tells us that:

 

1/5*P = s - 6

P = 5s - 30

 

I would take the two equations for P and set them equal to each other:

 

5s - 30 = 3s + 6

2s = 36

s = 18

 

The sides are then going to be 18, 20, 22. Add them up and you get your perimeter.