Réponse :
Bonjour
Explications étape par étape
P = 50 m
1) P = 2(L + l)
Si L = x alors on a :
50 = 2(x + l)
50/2 = x + l
l = 25 - x
2) A = 100 m^2 montrer que :
x^2 - 25x + 100 = 0
A = L * l
100 = x(25 - x)
100 = 25x - x^2
x^2 - 25x + 100 = 0
3) dimensions de la parcelle :
[tex]\Delta = (-25)^{2} - 4 \times 1 \times 100 = 625 - 400 = 225[/tex]
[tex]\sqrt\Delta = 15[/tex] > 0 donc deux solutions
X1 = (25 - 15)/2 = 10/2 = 5 m
X2 = (25 + 15)/2 = 40/2 = 20 m
largeur = 5 m
Longueur = 20 m
4) x + y = S
xy = P
y = S - x
y = P/x
S - x = P/x
xS - x^2 = P
x^2 - Sx + P = 0
