Question

In exchange of a square plot one of whose sides is 84 m, a man wants to buy a rectangular plot 144 m long and of the same area as of the square plot. Find the width of the rectangular plot.

Answer 1

$$\begin{gathered} \text{Given:} \\ \text{Side of the square plot = 84 m} \\ \text{Now, the man wants to exchange it with a rectangular plot of the same area with length 144.} \\ \mathrm{A}{\text{rea of the square plot = 84×84 = 7056 m}}^2 \\ \therefore \text{Area of the rectangular plot = Length×Width} \\ 7056=144\times \text{Width} \\ \Rightarrow \text{Width=}\frac{7056}{144}\text{=49 m} \\ \text{Hence, the width of the rectangular plot is 49 m.} \end{gathered}$$