Bonjour
30 ( x + 20 ) = 30 x + 600
aire rectangle = 30 x + 600
[( 30 + x ) * ( x + 20 ) ] / 2
( 30 x + 600 + x² + 20 x ) / 2
( x² + 50 x + 600 ) / 2
= 0.5 x² + 25 x + 300
aire miroir = 0.5 x ²+ 25 x + 300
0.5 x + 25 x +300 > ( 30 x + 600 ) * 9 /10
0.5 x² + 25 x + 300 > (270 x + 5 400 ) / 10
0.5 x² + 25 x + 300 > 27 x + 540
0.5 x² + 25 x - 27 x > 540 - 300
0.5 x² - 2 x > 240
0.5 x² - 2 x - 240 = 0
Δ = ( - 2 )² - 4 ( 0.5 * - 240 ) = 4 + 480 = 484 = 22 ²
x 1 = ( 2 - 22 ) / 1 = - 20 non retenu
x 2 = ( 2 + 22 ) / 1 = 24
valeur minimale = 24 cm
