bonsoir

P = 2 ( x + 2 x + 5 )

p =  2 x + 4 x + 10

P = 6 x + 10

6 x+ 10 = 31

6 x = 31 - 10

6 x = 21

x = 21/6  = 3.5  

largeur  =  3.5  cm

longueur  = 2 *3.5 + 5 = 12