The area of a rectangular plot is 528 m 2 . The length of the plot (in meters) is one meter more than twice its breadth. Find the length and the breadth of the plot

Given:
The area of rectangle

= 528 m 2

The length of the rectangle be ‘l’ and the breadth of the rectangle be ‘b’.
⇒

l = 2 b + 1

The area of rectangle =

l × b

\Rightarrow 528 = (2 b + 1) b

\Rightarrow 528 = 2 b^{2} + b

\Rightarrow 2 b^{2} + b - 528 = 0

\Rightarrow 2 b^{2} - 32 b + 33 b - 528 = 0

\Rightarrow 2 b (b - 16) + 33 (b - 16) = 0

\Rightarrow (2 b + 33) (b - 16) = 0

⇒

2 b + 33 = 0

b - 16 = 0

⇒

b = - \frac{33}{2}, 16

The breadth of a rectangle is always positive.
So, b = 16.
The length

⇒ 2 (16) + 1 m ⇒ 33 m

Hence, the length and breadth of the plot are 33m and 16m respectively.
So, the correct option is 3.

The area of a rectangular plot is 528 $m 2$ . The length of the plot (in meters) is one meter more than twice its breadth. Find the length and the breadth of the plot