This child likely has constitutional growth delay. Children with constitutional growth delay have a normal growth velocity.  There is often a family history of delayed puberty in a parent or a sibling.  Children will reach an appropriate final adult height that is within their genetic potential.  This diagnosis can be made often using history (including parental and siblings’ growth and pubertal history) and thorough physical examination.  If performed, a bone age X-ray will be delayed compared to chronologic age.  These children will be "late bloomers" who enter puberty later than average, but reach a final adult height in keeping with their genetic potential.  No treatment, other than reassurance, is needed.  

Failure to thrive: Current clinical concepts. Pediatrics in Review 2011; 32: 100-108.

Evaluation of short and tall stature in children.  American Family Physician 2008; 78(5): 597-604.