Final answer:
The length of DE is found by solving the equation DE + EF = DF with the given values, resulting in DE being 89 units.
Step-by-step explanation:
To find the length of DE when given DE = 8x + 1, EF = 20 - x, and DF = 98, we can use the fact that DE + EF = DF, since DE and EF are segments of DF. Let's substitute the given expressions into this equation:
- DE + EF = DF
- (8x + 1) + (20 - x) = 98
Simplify and solve for x:
- Combine like terms: 7x + 21 = 98
- Subtract 21 from both sides: 7x = 77
- Divide both sides by 7: x = 11
Now that we have the value of x, we can find the length of DE:
- DE = 8x + 1
- DE = 8(11) + 1
- DE = 88 + 1
- DE = 89
Therefore, the length of DE is 89 units.