Question

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

• A. 30 m and 10 m
• B. 35 m and 12 m
• C. 34 m and 15 m
• D. 33 m and 16 m

Answer 1

The correct option is D

33 m and 16 m

Let the breadth of the rectangular plot = $xm$
Hence, the length of the plot is $(2x+1)m$
Formula of area of rectangle = $length\times breadth=528m^2$
Putting the value of length and width, we get
$(2x+1)\times x=528$
$\Rightarrow 2x^2+x=528$
$\Rightarrow 2x^2+x-528=0$
$\Rightarrow 2x^2-32x+33x-528=0$
$\Rightarrow 2x(x-16)+33(x-16)=0$
$\Rightarrow (2x+33)(x-16)=0$
Either $2x+33=0orx-16=0$
$\Rightarrow x=-\frac{33}{2}orx=16$
As the length and breadth cannot be in negative values,
$x=16$, breadth = $16m$
Length $=2\times 16+1$

= $33m$