In this problem, we are going to apply the segement addition property. It simply states the following with respect to your problem:
From the diagram, we are given the following information:
Using the segment addition property, we can substitute the expressions for DE, EF, and DF to create and solve an equation:
Combine like terms of the left-hand side:
Add 20 to both sides of the equation:
Subtract 8x from both sides:
Divide both sides by 2:
Now we know the value of x is 13. We will use that to find DF:
The length of DF is 240 units.