m1) a. FD/FG = DJ/GM ⇒ DJ = (FD x GM)/FG = 6 x 3/18 = 18/18 = 1 cm
FA/FG = AI/GM ⇒ AI = FA x GM/FG = 12 x 3/18 = 2 x 6 x 3/3x 6 = 2 cm
DJ = 1 cm
AI = 2 cm
b. Calculer (FM)
Théorème de Pythagore : FM² = GM² + FG² = 3² + 18² = 9 + 324 = 333
FM = √333 = 18.25 cm on arrondis au dixième près
FM = 18.3 cm
d) calculer les aires des triangles FGM, FAI et FDJ
A(FGM) = 1/2 x DG x GM = (1/2) x 18 x 3 = (1/2) x 2 x 9 x 3 = 27 cm²
A(FAI) = 1/2 x FA x AI = (1/2) x 12 x 2 = 12 cm²
A(FDJ) = 1/2 x FD x DJ = (1/2) x 6 x 1 = 1/2 x 2 x 3 x 1 = 3 cm²
Que constate-t-on ?
A(FGM) = k² x A(FDJ) = 3² x 3 = 3³ = 27cm²
A(FAI) = k² x A(FDJ) = 2² x 3 = 12 cm²
e) calculer l'aire du quadrilatère BCJI
A(BCJI) = A(ABCD) - A(AIJD)
A(AIJD) = (1 + 2)/2 x 6 = 3/2 x 2 x 3 = 9 cm²
A(BCJI) = 36 - 9 = 27 cm²
2) x inconnue
a) GM = x/2
b) DJ = x * x/2/3x = x/6
AI = 2x * 1/2x)/3x = x/3
c) A(FGM) = 1/2)* 3x * x/2 = 3x²/4
A(FAI) = (1/2)* 2x *x/3 = x²/3
A(FDJ) = 1/2)* x *x/6 = x²/12
d) je vous laisse le soin de faire la vérification
