1. **Problem Statement:** Calculate the perimeter of pentagon ABCDE formed by two overlapping rectangles with given side lengths. 2. **Given Information:** - Length AE = 12 - Length BF = 16 - Right angle at B - Using Pythagoras theorem: $$16^2 + 12^2 = c^2$$ 3. **Calculate the diagonal length c:** $$c = \sqrt{16^2 + 12^2} = \sqrt{256 + 144} = \sqrt{400} = 20$$ 4. **Identify the sides of the pentagon:** - AB = BF = 16 (vertical side) - BC = 12 (horizontal side) - CD = 20 (diagonal side calculated) - DE = 12 (horizontal side) - EA = 12 (horizontal side) 5. **Calculate the perimeter:** $$P = AB + BC + CD + DE + EA = 16 + 12 + 20 + 12 + 12 = 72$$ 6. **Answer:** The perimeter of pentagon ABCDE is **72**. Therefore, the correct choice is (B) 72.