6) \(\frac{33}{4} : h = \frac{11}{12} : \frac{8}{9}\)

6) Решим пропорцию: \(\frac{33}{4} : h = \frac{11}{12} : \frac{8}{9}\)

\(\frac{33}{4} : h = \frac{11}{12} \cdot \frac{9}{8}\)

\(\frac{33}{4} : h = \frac{11 \cdot 9}{12 \cdot 8}\)

\(\frac{33}{4} : h = \frac{99}{96}\)

\(\frac{33}{4} : h = \frac{33}{32}\)

По правилу пропорции:

\(\frac{33}{4} \cdot \frac{33}{32} = h\)

\(h = \frac{33}{4} : \frac{33}{32}\)

\(h = \frac{33}{4} \cdot \frac{32}{33}\)

\(h = \frac{33 \cdot 32}{4 \cdot 33}\)

\(h = \frac{32}{4}\)

\(h = 8\)

Ответ: 8