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]$latex 8\sqrt{15} m$
[B]$latex 13 m$
[C]$latex 2\sqrt{30} m$
[D]$latex \sqrt{13} m$
$latex \mathbf{2\sqrt{30} m}$
Area of the rectangular garden $latex = 12 \times 5 = 60 m^{2}$
Area of the square garden $latex = 60 m^{2}$
∴ Side of the square garden $latex = \sqrt{60} m^{2}$
∴ Diagonal of the square garden $latex = \sqrt{2}\times Side$
$latex = \sqrt{2}\times \sqrt{60} = \sqrt{120}= \sqrt{4\times 30}$
$latex = 2\sqrt{30}m$
Hence option [C] is the right answer.