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Question Number 191639 by a.lgnaoui last updated on 28/Apr/23

$$\mathrm{Une}\mathrm{feuille}\mathrm{de}\mathrm{papier}\mathrm{format}\mathbf{A}4\mathrm{est}\mathrm{plie}$$$$\mathbf{n}\mathrm{fois}\mathrm{simultanement}\mathrm{en}\mathrm{longueur}\mathrm{et}$$$$\mathrm{largeur}(\mathrm{total}\mathrm{plie}=2\mathrm{n})$$$$-\mathrm{Quel}\mathrm{son}\mathrm{les}\mathrm{nouvelles}\mathrm{dimensions}\mathrm{de}\mathrm{cette}\mathrm{feuille}$$$$\mathrm{la}\mathrm{feuille}\mathrm{a}\mathrm{la}\mathrm{fin}.$$$$-\mathrm{quel}\mathrm{seront}\mathrm{ses}\mathrm{dimensions}\mathrm{apres}$$$$6\mathbf{pliages}$$$$-\mathrm{Quel}\mathrm{seront}\mathrm{les}\mathrm{dimensions}\mathrm{pour}\mathrm{une}\mathrm{feuille}\mathbf{care}\mathrm{de}30\mathbf{cm}$$$$\mathrm{plie}6\mathbf{fois}\mathrm{succrssivement}\mathrm{en}\mathrm{long}\mathrm{et}\mathrm{large}$$$$$$

Commented by a.lgnaoui last updated on 28/Apr/23

Answered by a.lgnaoui last updated on 29/Apr/23

$$1-\mathrm{dimensions}\mathrm{apres}\mathbf{n}\mathrm{plies}=\frac{21}{2\mathbf{n}}\mathrm{cm}\times \frac{29,7}{2\mathrm{n}}\mathrm{cm}$$$$2-\mathrm{apres}6\mathbf{pliages}\mathbf{n}=6$$$$\mathrm{dimensions}=\frac{21}{12}\mathrm{cm}\times \frac{29,7}{12}\mathrm{cm}$$$$\mathrm{ou}\frac{7}{4}\mathrm{cm}\times \frac{29,7}{12}\mathrm{cm}$$$$3-\mathrm{pour}\mathrm{feuille}\mathrm{de}30\mathrm{cm}\mathrm{plie}6\mathrm{fois}:$$$$\mathrm{dimensions}={\left(\frac{30}{12}\right)}^2=\frac{25}{4}$$$$$$

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