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(D) Let the width of the rectangular lawn be $w$ meters.Then,the length $l = 2w$ meters.The area of the lawn is given as $\frac{2}{3}$ hectares.Since

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$\frac{200}{\sqrt{3}}\,m$

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(D) Let the width of the rectangular lawn be $w$ meters.Then,the length $l = 2w$ meters.The area of the lawn is given as $\frac{2}{3}$ hectares.Since $1 	ext{ hectare} = 10,000 \, m^2$,the area is $\frac{2}{3} 	imes 10,000 = \frac{20,000}{3} \, m^2$.The area of a rectangle is $	ext{length} 	imes 	ext{width} = l 	imes w$.Substituting the values: $(2w) 	imes w = \frac{20,000}{3}$.$2w^2 = \frac{20,000}{3} \Rightarrow w^2 = \frac{10,000}{3}$.$w = \sqrt{\frac{10,000}{3}} = \frac{100}{\sqrt{3}} \, m$.The length $l = 2w = 2 	imes \frac{100}{\sqrt{3}} = \frac{200}{\sqrt{3}} \, m$.

$A$ lawn in the form of a rectangle has a length twice its width. The area of the lawn is $\frac{2}{3}$ hectares. The length of the lawn is:

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