bjr
Q1
aire AGH = 1/2 * AG * AH = aire triangle rectangle = 1/2 aire rectangle
donc
aire AGH = 1/2 * (8 - x) * x
soit (4 - 1/2x) * x = 4x - 1/2x² = -1/2x² + 4x = -1/2 (x² - 8x)
= -1/2 [(x - 4)² - 4²] = -1/2 (x - 4)² + 8
car le développement de (x - 4)² = x² - 8x + 4²
Q2
surface mauve = 32m²
soit surface mauve = surface ABD - aire de 4 triangles identiques
soit
8² - 4*( -1/2 (x - 4)² + 8) = 32
64 + 2 (x - 4)² - 32 = 32
2 (x - 4)² = 0
x = 4