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Réponse :

Explications étape par étape

Bonjour

Exercice 1 :

Aire : 4,5 cm^2

AB = 3 cm

Aire = AB x BC

4,5 = 3 x BC

BC = 4,5/3

BC = 1,5 cm

Théorème de thales :

MC/MD = ME/MA = EC/DA

1/(CD - CM) = EC/DA

1/(AB - 1) = EC/BC

1/(3 - 1) = EC/1,5

1/2 = EC/1,5

EC = 1,5/2

EC = 0,75 cm

Pythagore :

EC^2 + CM^2 = EM^2

0,75^2 + 1^2 = EM^2

0,5625 + 1 = EM^2

EM^2 = 1,5625

EM = 1,25 cm

MA^2 = MD^2 + DA^2

MA^2 = (3 - 1)^2 + 1,5^2

MA^2 = 2^2 + 1,5^2

MA^2 = 4 + 2,25

MA^2 = 6,25

MA = 2,5 cm

EA = EM + MA

EA = 1,25 + 2,5

EA = 3,75 cm

Exercice 2 :

Figure 1 :

x = 15 - 11

x = 4 cm

3y = 18

y = 18/3

y = 6 cm

18,75/15 = 1,25 (rapport d’agrandissement)

x = 4 * 1,25

x = 5 cm

y = 6 * 1,25

y = 7,5 cm