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A \(\begin{array}{l}
a)\,\,\,BH = 18cm\\BC = 40cm\\AC = 50cm\\
b)\,\,\,BD = 18,5cm.
\end{array}\)

B \(\begin{array}{l}
a)\,\,\,BH = 18cm\\BC = 50cm\\AC = 40cm\\
b)\,\,\,BD = 18,5cm.
\end{array}\)

C \(\begin{array}{l}
a)\,\,\,BH = 18cm\\BC = 50cm\\AC = 40cm\\b)\,\,\,BD = 22,5cm.\end{array}\)

D \(\begin{array}{l}
a)\,\,\,BH = 18cm\\BC = 40cm\\AC = 50cm\\
b)\,\,\,BD = 22,5cm.
\end{array}\)

A \(AB = 4cm;\,\,AC = 6\,cm;\,\,BC = 2\sqrt {13} \,cm\)

B \(AB = 2cm;\,\,AC = 3\,\,cm;\,\,BC = \sqrt {13} \,cm\)

C \(AB = 2\sqrt {15} cm;\,\,AC = 3\sqrt {15} \,\,cm;\,\,BC = 5\sqrt {15} \,cm\)

D \(AB = 2\sqrt {13} cm;\,\,AC = 3\sqrt {13} \,\,cm;\,\,BC = 13cm\)

A \(\begin{array}{l}
a)\,\,\frac{{HB}}{{HC}} = \frac{9}{{25}}\\
b)\,\,\,AH \approx 42
\end{array}\)

B \(\begin{array}{l}
a)\,\,\frac{{HB}}{{HC}} = \frac{16}{{25}}\\
b)\,\,\,AH \approx 42
\end{array}\)

C \(\begin{array}{l}
a)\,\,\frac{{HB}}{{HC}} = \frac{25}{{16}}\\
b)\,\,\,AH \approx 42
\end{array}\)

D \(\begin{array}{l}
a)\,\,\frac{{HB}}{{HC}} = \frac{25}{{9}}\\
b)\,\,\,AH \approx 42
\end{array}\)