slts

ex 6

AB = 12 cm

BC = 8 cm

aire AEIG = x * x = x²

aire IHCF = IH * HC = (AB - x) (BC - x)

résoudre

x² = (12-x) (8-x)

x² = 96 - 12x - 8x + x²

20x = 96

x = 4,8 cm

vérif

aire AEIG = 4,8² = 23,04 cm²

et

aire IHCF = (12 - 4,8) (8 - 4,8) = 7,2 * 3,2 = 23,04 cm²