Final answer:
The Ottoman Empire doubled its land during the a.15th century, with a substantial expansion after the conquest of Constantinople in 1453.
Step-by-step explanation:
The period during which the Ottoman Empire doubled its land was the a.15th century.
The empire, which was established in the late 13th century, experienced rapid expansion during the 15th century.
After conquering Constantinople in 1453, successive rulers expanded the empire into southeastern Europe, the Middle East, and North Africa.
The pinnacle of Ottoman expansion was reached during the reign of Sultan Suleiman I in the 16th century.
However, it was in the 15th century when the empire's land holdings saw a significant and expansive increase.