bonjour,
3) calcul des bases
BC=6 QR=x
calcul hauteur
RB=100-x
A= 1/2( BC +QR)xRB
A=1/2(60+x)(100-x)
A=1/2(6000+100x-60x-x²)
A=1/2(-x²+40x+6000
A= -0.5x²+20x+3000
4)Aire du rectangle 60x100=6000
1/2A=3000
-0.5x²+20x+3000=3000
-0.5x²+20x=0
x(-0.5x+20)=0
x=0
-0.5x+20=0 -0.5x=-20 0.5x=20 x=40
5)-0.5x²+20x+3000=-0.5(x²-40x)+300
-0.5( x²-40x+400)-400+3000
-0.5(x-20)²+2600
6)A=3100
-0.5(x-20)²+2600=3100
-0.5(x-20)²=500
(x-20)²=500/-0.5
500/-0.5<0
impossible que (x-20)²<0
valeur maximale
-0.5x²+20x+3000
abscisse =-b/2a =-20/-0.5x2 = 20/1=20
x=20 donnera la valeur maximale
si x=20 alors A=-0.5(x-20)+2600
A= 2600
