The area of a rectangular plot of land is $46\dfrac{2}{5}$ sq.m. If its length is $7\dfrac{1}{4}$ m, find its breadth.

Given, the area of a rectangular plot of land = $46\dfrac{2}{5}$ sq. m

Length of rectangular plot = $7\dfrac{1}{4}$ m

Let b be the breath of the rectangular plot.

By formula, length x breadth = area

$\Rightarrow 7\dfrac{1}{4} \times b = 46\dfrac{2}{5}\\[1em] \Rightarrow \dfrac{29}{4} \times b = \dfrac{232}{5}\\[1em] \Rightarrow b = \dfrac{232}{5} ÷ \dfrac{29}{4}\\[1em] \Rightarrow b = \dfrac{232}{5} \times \dfrac{4}{29}\\[1em] \Rightarrow b = \dfrac{232 \times 4}{5 \times 29}\\[1em] \Rightarrow b = \dfrac{232}{29} \times \dfrac{4}{5} \\[1em] \Rightarrow b = 8 \times \dfrac{4}{5} \\[1em] \Rightarrow b = \dfrac{32}{5}\\[1em] \Rightarrow b = 6\dfrac{2}{5}.$

Hence, the breadth of the rectangular plot = $6\dfrac{2}{5}$ m.