Answer:
5s = 85
Step-by-step 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
<em>(If you wanted to solve for s, just divide both sides by 5)</em>
<em>5s / 5 = 85 / 5</em>
<em>s = 17</em>
