If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the rectangle is reduced by 80 cm^2. However,…

Let the length of rectangle be x cm and the breadth be y cm Area of rectangle = xy \[\begin{aligned} & (x-5)(y+2)=x y-80 \Rightarrow 2 x-5 y+70=0 \\ & (x+10)(y-5)=x y+50 \Rightarrow-5 x+10 y-100=0 \end{aligned} \] Solving the two equations, we get \[\begin{aligned} & x=40 \text { and } y=30 \\ & \therefore \text { Length of rectangle }=40 \mathrm{~cm} \\ & \text { and Breadth of rectangle }=30 \mathrm{~cm} \end{aligned} \]