Bonjour,

3) Si tu as bien appris ton cours, je ne vais pas te réexpliquer le théorème de Pythagore.

a)

[tex]GP^{2} = PH^{2} + GH^{2} \\PH^{2} = GP^{2} - GH^{2} \\\\PH^{2} = 7,5^{2} - 6^{2} \\\\PH^{2} = 56,25 -36 \\\\PH^{2} = 20,25\\PH = \sqrt{20,25} \\PH = 4,5[/tex]

PH = 4,5 cm.

b)

[tex]PW^{2} = HW^{2} + PH^{2} \\PW^{2} = 2,8^{2} + 4,5^{2} \\PW^{2} = 7,84 + 20,25\\PW^{2} = 28,09\\PW = \sqrt{28,09} \\PW = 5,3[/tex]

PW = 5,3 cm.

c) Si PGW est rectangle alors :

[tex]WG^{2} = PG^{2} + PW^{2} \\8,8^{2} = 7,5^{2} + 5,3^{2} \\\\8,8^{2} = 56,25 + 28,09 \\\\\\8,8^{2} = 84,34\\\\\\8,8 = \sqrt{84,34} \\8,8 = 9,183681179135086[/tex]

PGW n'est pas rectangle.

4)

a)

Romain = [tex]\frac{1}{4} = \frac{1*2}{4*2} = \frac{2}{8}[/tex]

Maëlia = [tex]\frac{3}{8}[/tex]

[tex]\frac{2}{8} + \frac{3}{8} = \frac{5}{8}[/tex]

Ils ont mangés [tex]\frac{5}{8}[/tex] du gâteau.

b)

[tex]\frac{8}{8} - \frac{5}{8} = \frac{3}{8}[/tex]

Il reste [tex]\frac{3}{8}[/tex] du gâteau.

5)

A = [tex]\frac{2*4}{2} +\frac{5}{2} = \frac{8}{2} + \frac{5}{2} = \frac{13}{2}[/tex]

B = [tex]\frac{6}{7} + \frac{2}{35} = \frac{6*5}{7*5} + \frac{2}{35} = \frac{30}{35} + \frac{2}{35} = \frac{32}{35}[/tex]

C = [tex]\frac{13}{7} - \frac{13}{5} = \frac{13*5}{7*5} - \frac{13*7}{5*7} = \frac{65}{35} - \frac{91}{35} = \frac{-26}{35}[/tex]

D = [tex]\frac{3}{35} -\frac{13}{21} = \frac{3*3}{35*3} -\frac{13*5}{21*5} = \frac{9}{105} -\frac{65}{105} = \frac{-56}{105} = \frac{-56/7}{105/7} = \frac{-8}{15}[/tex]