The length of a plot is five times its breadth. A playground measuring 245 square meters occupies half of the total area of the plot. What is the length of the plot?

The length of a plot is five times its breadth. A playground measuring 245 square meters occupies half of the total area of the plot. What is the length of the plot?
[A]5\sqrt{2} m
[B]175\sqrt{2} m
[C]35\sqrt{2} m
[D]490 m

\mathbf{35\sqrt{2} m}
Let breadth of plot = x m
∴ lenght = 5x m
As per the question,
\frac{5x^{2}}{2} = 245
=> x^{2} = \frac{245\times 2}{5} = 98
=> x = 7 \sqrt{2} m
\therefore length = 5\times 7\sqrt{2} = 35\sqrt{2}m
Hence option [C] is the right answer.

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