Question

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: Cross - multiply the proportion

We have the proportion $\frac{4}{11}=\frac{2}{HD}$. Cross - multiplying gives us $4\times HD = 11\times2$.

Step2: 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)