Why does anorexia nervosa present with hypothyroidism, amenorrhea, osteoporosis, lanugo?

Why does anorexia nervosa present with hypothyroidism, amenorrhea, osteoporosis, lanugo?

It actually causes euthyroid sick syndrome and decrease in T3.

Amenoerhea is due to functional hypothalamic amenorrhea(decreased leptin causes to shut down GnRH secretion and hence decreases FSH,LH=decreased estrogen=Anovulation),same mechanism of osteoporosis(decreased estrogen).

Thank you very much!