#### Question

The area of a rectangular plot is 528 m^{2}. The length of the plot (in metres) is one metre more then twice its breadth. Find the length and the breadth of the plot.

#### Solution

Let the breadth of the rectangular plot be *x *m.

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

According to the question,

Length × Breadth = Area

\[x(1 + 2x) = 528\]

\[ \Rightarrow 2 x^2 + x - 528 = 0\]

\[ \Rightarrow 2 x^2 + 33x - 32x - 528 = 0\]

\[ \Rightarrow x(2x + 33) - 16(2x + 33) = 0\]

\[ \Rightarrow (x - 16)(2x + 33) = 0\]

\[ \Rightarrow x - 16 = 0 \text { or } 2x + 33 = 0\]

\[ \Rightarrow x = 16 \text { or } x = - \frac{33}{2}\]

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.