The perimeter of a rectangular field is $\dfrac{3}{5}$ km. If the length of the field is twice its width; find the area of the rectangle in sq. metres.

Given:

Perimeter = $\dfrac{3}{5}$ km.

Length of the field = Twice its width.

Let a be the width of the field.

So, the length = 2a

Perimeter of a rectangle = 2(length + width)

$⇒ \dfrac{3}{5} = 2(2a + a)\\[1em] ⇒ \dfrac{3}{5} = 2 \times 3a\\[1em] ⇒ \dfrac{3}{5} = 6a\\[1em] ⇒ a = \dfrac{3}{5 \times 6}\\[1em] ⇒ a = \dfrac{3}{30}\\[1em] ⇒ a = \dfrac{1}{10}\\[1em]$

Thus, width = $\dfrac{1}{10}$ km

= $\dfrac{1}{10} \times 1,000$ m

= 100 m

Length = 2a = 2 x 100 m

= 200 m

Area = length x width

= 200 x 100 m²

= 20,000 m²

Hence, the area of the rectangle is 20,000 m².