Bonjour,
1) Sur la figure, x = BH = AD, donc il faut que x ≥ 3 car :
AD = BC = BG + GC et GC = 3
Donc :
x = 2 non
x = 5 oui
x = 9 oui
x = 12 non car il faut x ≤ AB donc x ≤ 12
2) AH = 12 - x = 12 - 5 = 7 cm
et AD = x = 5 cm
Donc P = 2 x (7 + 5) = 24 cm
et A = 7 x 5 = 35 cm²
3)
BC = AD = x
AH = AB - HB = DC - HB = 12 - x
CG = CB - GB = AD - GB = x - 3
4)
P(ABCD) = 2(AB + AD) = 2(12 + x)
A(ABCD) = AB x AD = 12x
P(EFCG) = 2(EF + EC) = 2[(x - 3) + x] = 2(2x - 3)
A(EFCG) = EF x EC = x(x - 3)
P(ABGFED) = AB + BG + GF + FE + ED + DA
= 12 + 3 + x + (x - 3) + (12 - x) + x
= 24 + 2x
A(ABGFED) = A(ABCD) - A(EFCG)
= 2(12 + x) - x(x - 3)
= 24 + 2x - x² + 3x
= -x² + 5x + 24
5) A = -(x - 8)(x + 3)
6) Aire d'un rectangle = Longueur x largeur = l * x
On veut : lx = A
Donc l = A/x = -(x - 8)(x + 3)/x
7) KN = UM = l = -(x - 8)(x + 3)
