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
