The area of a rectangular plot of land is $817\dfrac{4}{5}$sq. m. If its breadth is $21\dfrac{3}{4}$m, find its length.

Given:

Area of rectangular plot of land = $817\dfrac{4}{5}\text{ m}^2 = \dfrac{4089}{5}\text{ m}^2$

Breadth = $21\dfrac{3}{4}\text{ m} = \dfrac{87}{4} \text{ m}$

Length of rectangular plot of land = ?

Length of rectangular plot of land = (Area of rectangular plot of land) ÷ (Breadth)

Substituting the values in above, we get:

Length of rectangular plot of land = $\dfrac{4089}{5}\text{ m}^2 ÷ \dfrac{87}{4} \text{ m}$

$\begin{array}{ll} = \Big(\dfrac{4089}{5} \times \dfrac{4}{87}\Big)\text{ m} & [\text{Reciprocal of } \dfrac{87}{4} \text{ is } \dfrac{4}{87}] \\ = \Big(\dfrac{47}{5} \times \dfrac{4}{1}\Big)\text{ m} & \text{[Simplifying 2565 and 345 ⇒ Divide by 15]} \\ = \dfrac{47 \times 4}{5 \times 1} \text{ m} \\ = \dfrac{188}{5} \text{ m} \\ = 37\dfrac{3}{5}\text{ m} \end{array}$

∴ The breadth of rectangular plot of land = $37\dfrac{3}{5}$ m