A

B

C

D

M

N

AD=4

AB=6

On\ pose\ x=BM=CN.\
Pour\ quelle\ valeur\ de\ x\ les\ triangles\ ABM\ et\ ADN\ ont-ils\ des\ aires\ égales\ ?

Equation : rectangle\ et\ deux\ triangles

Calculés\ par\ geogebra :

Mise\ en\ équation : \frac {x \times 6}{2}=\frac {(6-x)\times 4}{2}\
Résolution :  \frac {x \times 6}{2}=\frac {(6-x)\times 4}{2}\Leftrightarrow 6x=24-4x \Leftrightarrow 10x=24\Leftrightarrow x=\frac {24}{10}\ \Leftrightarrow x=2,4 

Afficher une aide à la résolution

(d'après\ brevet )

A = (-5.005646218114844, 3.2390633654525596)
a = 1 (slider from 0 to 4, step 0.1)
B = Point(Circle[A, 6])
a_2 = Segment(A, B)
b = OrthogonalLine(B, a_2)
c = Circle(B, 4)
C = Intersect(c, b, 2)
d = OrthogonalLine(C, b)
e = OrthogonalLine(A, a_2)
D = Intersect(d, e)
poly1, a_1, b_1, c_1, d_1 = Polygon(A, B, C, D)
f = Circle(B, a)
M = Intersect(f, b, 2)
g = Circle(C, a)
E = Intersect(d, c_1)
F = Intersect(d, c_1)
N = Intersect(g, d, 2)
poly2, m, a_3, b_2 = Polygon(A, B, M)
poly3, d_2, a_4, n = Polygon(A, N, D)
texte9: "BM=CN=" + (LaTeX[a]) + ""
h = Segment(B, M)
texte8: "Les\ deux\  triangles\ ont \ la\  même\  aire \ lorsque : x=" + (LaTeX[a]) + ""
i = Segment(B, M)
j = Segment(C, N)
k = Segment(C, N)
G = Midpoint(A, D)
H = Midpoint(A, B)
α, β, γ, δ = Angle(poly1)
texte10: "\mathcal {A}_{ADN}=" + (LaTeX[poly3]) + ""
texte11: "\mathcal {A}_{ABM}=" + (LaTeX[poly2]) + ""
l = false