Question

The area of a rectangular plot is 528 m². The length of the plot (in metres) is one metre more then twice its breadth. Find the length and the breadth of the plot.

Answer 1

Let the breadth of the rectangular plot be x m.
Then, the length of the rectangular plot = (1 + 2x) m.

According to the question,

Length × Breadth = Area
$$\begin{gathered} x(1+2x)=528 \\ \Rightarrow 2x^2+x-528=0 \\ \Rightarrow 2x^2+33x-32x-528=0 \\ \Rightarrow x(2x+33)-16(2x+33)=0 \\ \Rightarrow (x-16)(2x+33)=0 \\ \Rightarrow x-16=0\mathrm{or}2x+33=0 \\ \Rightarrow x=16\mathrm{or}x=-\frac{33}{2} \end{gathered}$$

Since, length and breadth of the rectangle cannot be negative.

Thus, the breadth of the rectangular plot is 16 m.

and the length of the rectangular plot is (1 + 2×16) = 33 m.