Answer:
• DC=83.6 units
,
• DF = 33.5 units
Explanation:
From the diagram:
The length of each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
[tex]\begin{gathered} \frac{FC}{DC}=\frac{DC}{EC} \\ \implies\frac{72}{DC}=\frac{DC}{97} \\ DC^2=72\times97 \\ DC=\sqrt[]{72\times97} \\ DC=83.6\text{ units} \end{gathered}[/tex]
Similarly:
[tex]\begin{gathered} \frac{ED}{FD}=\frac{FD}{DC} \\ \frac{97-83.6}{DF}=\frac{DF}{83.6} \\ \frac{13.4}{DF}=\frac{DF}{83.6} \\ DF^2=13.4\times83.6 \\ DF=\sqrt[]{13.4\times83.6} \\ DF=33.5\text{ units} \end{gathered}[/tex]
