Question

applying the side-splitter theorem
complete the work to find the length of \\(\overline{hd}\\).
use the side-splitter theorem to set up a proportion.
\\(\frac{eg}{gd} = \frac{fh}{hd}\\)
substitute in the known side lengths.
\\(\frac{4}{11} = \frac{2}{hd}\\)
cross-multiply and solve for hd.
hd = \\(\square\\)

Explanation:

Step1: Start with the proportion

We have the proportion $\frac{4}{11} = \frac{2}{HD}$.

Step2: Cross - multiply

Cross - multiplying gives us $4\times HD=11\times2$.

Step3: Solve for HD

Simplify the right - hand side: $4\times HD = 22$. Then divide both sides by 4: $HD=\frac{22}{4}=\frac{11}{2} = 5.5$.

Answer:

$\frac{11}{2}$ (or 5.5)