Answer:
5s = 85
Explanation:
Perimeter of our triangle = DE + EF + DF = 81 units
We know from the question that
The length of side DE is twice the length of side EF
DE = 2EF
and the length of side DF is 4 units less than the length of side DE
DF = DE - 4
We can replace EF with s in our equations
DE = 2s
And now we can replace DE from the other equation
DF = DE - 4
DF = 2s - 4
If the perimeter of our triangle = DE + EF + DF = 81 units
We will replace the sides with our new values
Perimeter = 2s + s + 2s - 4 = 81
We can put this as our answer, or we can simplify further
Simplify by adding 4 to both sides
2s + s + 2s - 4 + 4 = 81 + 4
Simplify
2s + s + 2s = 85
Simplify
5s = 85
Since the question only asked for an equation, not for us to solve it, we can stop here
(If you wanted to solve for s, just divide both sides by 5)
5s / 5 = 85 / 5
s = 17