# 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.