exercice 1.
1° trapèze
2°Aire du trapèze = (MN +BC)/2.BM
BM = 4 + x
BC = rac(25 - 16) = 3
MN/BC = x/4 => MN = 3/4.x
Aire BCMN = (3+ 3/4x)/2.(4+x) = (12 + 3x)(x+4)/8 = 3/8(x² + 8x + 16)
3° 3/8(x² + 8x + 16) = 27/2 => x² + 8x + 16 = 36 => x² + 8x - 20 = 0
racines 2 et -10 (à rejeter) donc pour x = 2
exercice 2
1° AM/AB = AN/AC =2/x
AM/AB = 2/x => AB/AM = x/2 => AB = x²/2
AN/AC =2/x => AC/6 = x/2 => AC = 3x
périmètre = x²/2 + 3x + 2x = (x² + 10x)/2
2° x² + 10 x - 24 = (x+5-7)(x+5+7) =(x-2)(x+12) = x² + 10x - 24
