The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden :

The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden :
[A]8\sqrt{15} m
[B]13 m
[C]2\sqrt{30} m
[D]\sqrt{13} m

\mathbf{2\sqrt{30} m}
Area of the rectangular garden = 12 \times 5 = 60 m^{2}
Area of the square garden = 60 m^{2}
∴ Side of the square garden = \sqrt{60} m^{2}
∴ Diagonal of the square garden = \sqrt{2}\times Side
= \sqrt{2}\times \sqrt{60} = \sqrt{120}= \sqrt{4\times 30}
= 2\sqrt{30}m
Hence option [C] is the right answer.

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