A rectangle field is half as wide as it is long and is completely encl

1.	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
Answer» (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

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

Answer»

(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