Halo 4 epilogue(campaign spoilers)

Well in the end of the campaign, master chief walks past sarah palmer. When she say master chief her jaw dropped and they show that he managed to grow 3-4 feet taller by the end of the campaign. In the mission where master chief meets sarah palmer for the first time, sarah palmer is up to his shoulder. So how did master chief get so tall? My guess is that when the librarian accelerated master chief’s evolution, he got a growth spurt that made him the size of an evolved human. Discuss.