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Sasa1109
@Sasa1109
April 2019
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Le demi périmètre d'une cour rectangulaire est de 130m.
En augmentant la longueur de la cour de 5m et en diminuant sa largeur de 3m, on augmente son aire de 135 mètres carrés.
Quelles sont les dimensions de la cour ?
merci
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Commentaires (10)
X =longueur
y = largeur
x+y = 130
x = -y+130
aire initiale =xy
on augmente x de 5,on diminue y de 3
(x+5)(y-3) = xy+135
on sait que y = -x+130
(x+5)(-x+130) = x(-x+130)+135
-x²+130x-5x+650 = -x²+130x+135
-x²+125x+650 = -x²+130x+135
-x²+x²+125x-130x = 135-650
-5x = -515
x = 103
x+y = 130
103+y = 130
y = 130-103
y = 27
L = 103m
l = 27m
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Lista de comentários
y = largeur
x+y = 130
x = -y+130
aire initiale =xy
on augmente x de 5,on diminue y de 3
(x+5)(y-3) = xy+135
on sait que y = -x+130
(x+5)(-x+130) = x(-x+130)+135
-x²+130x-5x+650 = -x²+130x+135
-x²+125x+650 = -x²+130x+135
-x²+x²+125x-130x = 135-650
-5x = -515
x = 103
x+y = 130
103+y = 130
y = 130-103
y = 27
L = 103m
l = 27m