Answer:
7.06 units
Explanation:
The given side lengths are indicated in the diagram below:
Using similar triangles, we have:
[tex]\begin{gathered} \frac{GF}{8}=\frac{8}{17} \\ 17GF=64 \\ GF=\frac{64}{17} \\ GF=3.76 \end{gathered}[/tex]
Next, apply Pythagorean Theorem to triangle DGF.
[tex]\begin{gathered} DG^2=DF^2+GF^2 \\ 8^2=DF^2+3.76^2 \\ DF^2=8^2-3.76^2 \\ DF^2=49.8624 \\ DF^{}=\sqrt{49.8624} \\ DF\approx7.06\text{ units} \end{gathered}[/tex]
The length of DF is approximately 7.06 units (to the nearest hundred).
