2024 AMC 10A Problems/Problem 16

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Problem

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 $AB$?

[img]https://cdn.artofproblemsolving.com/attachments/3/b/298cf96ec8fc90c438e4936a05c260170eda01.png[/img]

$\textbf{(A) }4+4\sqrt5\qquad\textbf{(B) }10\sqrt2\qquad\textbf{(C) }5+5\sqrt5\qquad\textbf{(D) }10\sqrt[4]{8}\qquad\textbf{(E) }20$