Question

Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is $528m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Answer 1

Let breadth of a plot is $xm$
According to question,
Length of plot $=(2\times breadth)+1=(2\times x+1)=(2x+1)m$.
Area of rectangular plot $=l\times b=(2x+1)\times x=(2x^2+x)sq.m$
Given: Area of plot $=528sq.m$
$2x^2+x=528$
$\Rightarrow 2x^2+x-528=0$
Required quadratic equation is :
$2x^2+x-528=0$
$\Rightarrow 2x^2+33x-32x-528=0$
$\Rightarrow x(2x+33)-16(2x+33)=0$
$\Rightarrow (2x+33)(x-16)=0$
$\Rightarrow x-16=0$ or $2x+33=0$
$\Rightarrow x=16$ or $x=\frac{-33}{2}$ ( impossible )
Hence, Length of plot is $2x+1=2\times 16+1=33m$
and breadth is $16m$