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in Perimeter and Area of Plane Figures by (46.2k points)
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A rectangle field is half as wide as it is long and is completely enclosed by x metre of fencing. What is the area of the field?

(a) \(\frac{x^2}{2}\) m2

(b) 2x2 m2

(c)   \(\frac{2x^2}{9}\) m2

(d)   \(\frac{x^2}{18}\) m2

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(d)   \(\frac{x^2}{18}\) m2

Let the breadth of the rectangular field be a m. Then, its length = 2a m

Given, 2(2a + a) = x ⇒ 6a = x ⇒ a = \(\frac{x}{6}\) m

∴ Length = 2a = 2 x \(\frac{x}{6}\) = \(\frac{x}{3}\) m

∴ Area of the rectangular field = \(\frac{x}{3}\) x \(\frac{x}{6}\) =   \(\frac{x^2}{18}\) m2

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