2024 AMC 10A Problem 16

All of the rectangles in the figure below, which is drawn to scale, are similar to the enclosing rectangle. Each number represents the area of the rectangle. What is length ABAB?
Rectangle subdivided into similar rectangles with areas 36, 32, 16, 4, 2, 25, 8, 9, 1, 18, and 49
(A)  4+45\text{(A)}\;4+4\sqrt{5}(B)  102\text{(B)}\;10\sqrt{2}(C)  5+55\text{(C)}\;5+5\sqrt{5}(D)  1084\text{(D)}\;10\sqrt[4]{8}(E)  20\text{(E)}\;20