The breadth ‘b’ of a room is twice its height and half of its length. Find the length of the longest diagonal of the room.

1
\(\frac{\sqrt{20} b}{2}\)
2
\(​​​​\frac{b}{2}\)
3
\(​​​​\frac{\sqrt{21}b}{2}\)
4
\(​​​​\frac{\sqrt{19}b}{2}\)

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