When the length of the rectangular plot is increased by four times its perimeter becomes 480 meters and area becomes 12800 sq.m. What is its original length(in meters)?

Let the length of the plot be $$l$$ meters and breadth = $$b$$ meters

New length = $$4l$$ meters

Perimeter = $$2(4l+b)=480$$

=> $$4l+b=\frac{480}{2}=240$$

=> $$b=240-4l$$ ---------(i)

Area = $$(4l \times b)=12800$$

=> $$lb=\frac{12800}{4}=3200$$

Substituting value of $$b$$ from equation (i)

=> $$l(240-4l)=3200$$

=> $$240l-4l^2=3200$$

=> $$l^2-60l+800$$

=> $$l=\frac{-(-60) \pm \sqrt{(-60)^2-(4 \times 1 \times 800)}}{2}$$

=> $$l=\frac{60 \pm \sqrt{3600-3200}}{2} = \frac{60 \pm \sqrt{400}}{2}$$

=> $$l=\frac{60 \pm 20}{2}$$

=> $$l=\frac{60+20}{2},\frac{60-20}{2}$$

=> $$l=\frac{80}{2},\frac{40}{2}$$

=> $$l=40,20$$ meters

=> Ans - (D)