F4 MATHS 求高手指教~

By Pythagoras thm.,
AB^2 = AP^2 + BP^2
(x + 6)^2 = x^2 + BP^2
x^2 + 36 + 12x = x^2 + BP^2
so BP = sqrt [36 + 12x]
B'C = BC - 2BP = 4x + 3 - 2 sqrt[36 + 12x] which is equal to AB since the figure is a rhombus.
So 4x + 3 - 2 sqrt[36 + 12x] = x + 6
2 sqrt [ 36 + 12x] = 3x - 3
4(36 + 12x) = (3x - 3)^2
144 + 48x = 9x^2 + 9 - 18x
9x^2 - 66x - 135 = 0
3x^2 - 22x - 45 = 0
(3x + 5)(x - 9) = 0
x = 9 (x = -5/3 is rejected)
So AB = 9 + 6 = 15 = B'C
So area of rhombus = height x B'C = 9 x 15 = 135 cm^2.