Question

Represent the following situations in the form of quadratic equations.
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. breadth = $16m$, length = $33m$
• B. breadth = $46m$, length = $33m$
• C. breadth = $16m$, length = $63m$
• D. breadth = $16m$, length = $93m$

Answer 1

The correct option is A

breadth = $16m$, length = $33m$

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,
hence, $x=16$, breadth = $16m$
length $=2\times 16+1$
= $33m$