Odpowiedź:
|BC| = 40 cm, |IJ| = 6 cm, |OM| = 7,7 cm
Szczegółowe wyjaśnienie:
Korzystamy z twierdzenia Talesa:
[tex]a\parallel b\quad\implies\quad\frac{|BC|}{|ED|}=\frac{|AB|}{|AE|}\\\\\frac{|BC|}{30}=\frac{36}{27}\qquad/\cdot30\\\\|BC|=\frac43\cdot30\\\\|BC|=40\,cm[/tex]
[tex]c\parallel d\quad\implies\quad\frac{|IJ|}{|HJ|}=\frac{|FI|}{|GH|}\\\\\frac{|IJ|}{9}=\frac{10}{15}\qquad/\cdot9\\\\|IJ|=\frac23\cdot9\\\\|IJ|=6\,cm[/tex]
[tex]e\parallel f\quad\implies\quad\frac{|NM|}{|LM|}=\frac{|ON|}{|KL|}\\\\\frac{|NM|}{6,4}=\frac{3,3}{4,8}\qquad/\cdot6,4\\\\|NM|=\frac{3,3\cdot6,4}{4,8}\\\\ |NM|=\frac{3,3\cdot4}{3}\\\\ |NM|=1{,}1\cdot4\\\\|NM|=4{,}4\ cm\\\\\\|OM|=|ON|+|NM|=3{,}3\ cm+4{,}4\ cm=7{,}7\ cm[/tex]
