Question

A square field of 2 sq km area is to be divided into two equal parts by a fence which concides with a diagonal. The length of the fence is?

Answer 1

$Let \: the \: side \:of \:a \: square \: field = s \:cm$

$Area \:of \:the \:field = 2 km^{2} \:(given)$

$\implies s^{2} = 2 \:km^{2}$

$\implies s^{2} = \Big(\sqrt{2 \:km}\Big)^{2}$

$\implies s = \sqrt{2} \:km \: --(1)$

$Now, \: Length \:of \:the \:fencing \\= Perimeter \:of \:the \:field + length \:of \: diagonal\\= 4s + 2\sqrt{s} \\= 4\sqrt{2} + 2 \times \sqrt{2} \\= 4\sqrt{2} + 2 \sqrt{2} \\=6\sqrt{2} \:km$

Therefore.,

$\red {Length \:of \:the \:fencing}\green {= 6\sqrt{2} \:km}$

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