Question

The area of a rectangle gets reduced by 67 square metres, when its length is increased by 3 m and breadth is decreased by 4 m.
If the length is reduced by 1 m and breadth is increased by 4 m, the area is increased by 89 square metres. Find the dimensions of the rectangle.

Answer 1

Let the length and breadth of the rectangle be x m and y m respectively.
Case1: When length is increased by 3 m and breadth is decreased by 4 m
$$\begin{gathered} xy-\left(x+3\right)\left(y-4\right)=67 \\ \Rightarrow xy-xy+4x-3y+12=67 \\ \Rightarrow 4x-3y=55.....\left(i\right) \end{gathered}$$
Case2: When length is reduced by 1 m and breadth is increased by 4 m
$$\begin{gathered} \left(x-1\right)\left(y+4\right)-xy=89 \\ \Rightarrow xy+4x-y-4-xy=89 \\ \Rightarrow 4x-y=93.....\left(ii\right) \end{gathered}$$
Subtracting (i) from (ii), we get
$2y=38\Rightarrow y=19$
Now, putting y = 19 in (ii), we have
$$\begin{gathered} 4x-19=93 \\ \Rightarrow 4x=93+19=112 \\ \Rightarrow x=28 \end{gathered}$$
Hence, length = 28 m and breadth = 19 m.