The base of a triangle is of length b, and the altitude is of length h. A rectangle of height x is inscribed in the triangle with the base of the rectangle in the base of the triangle. The area of the rectangle is:
a) \(\frac{bx}{h}(h-x)\) b) \(\frac{hx}{b}(b-x)\) c) \(\frac{bx}{h}(h-2x)\) d) \(x(b-x)\) e) \(x(h-x)\)