Bonjour,
Dcm => demi cercle de diametre [CM]
Dmb => demi cercle de diametre [MB]
Dcm + Dmb = 12,5π
Dcm = [(x/2)²×π]/2
Dmb = [((10-x)/2)×π]/2
On a alors :
[(x/2)²×π]/2 + [((10-x)/2)²×π]/2 = 12,5π
[(x/2)²×π]+ [((10-x)/2)²×π] = 12,5π
×2
[(x/2)²×π] + [((10-x)/2)²×π = 25π
π×[(x/2)²+((10-x)/2)²] = 25π
(x/2)²+((10-x)/2)²= 25
x²/4 + (100-20x+x²)/4= 25
(2x²-20x+100)/4 =
2x²-20x+100 = 100
2x²-20x = 0
2x(x-10) = 0
Soit 2x = 0 => x = 0
Soit x-10 = 0 => x = 10
Bonne journée !
