Question

Represent the following situation in the form of the quadratic equation:
The area of a rectangular plot is $528m^2$. The length of the plot is one metre more than twice its breadth. We need to find the length and breadth of the plot.

Answer 1

Let the breadth of the rectangular plot (b) be ${}^{\prime }{x}^{\prime }m.$

Then the length of the plot is one more than twice its breadth,

∴ Length (l)$=2x+1m.$

But Length $\times$ Breadth = Area of rectangle

$l\times b=A$

∴ $x\times (2x+1)=528sq.m.$

$2x^2+x=528$

∴ $2x^2+x–528=0$ is the required equation.

Now, we have to find out the value of ‘x’ :

$2x^2+x–528=0$

$2x^2–32x+33x–528=0$

$2x(x–16)+33(x–16)=0$

$(x–16)(2x+33)=0$

If $x–16=0$, then $x=16$

If $2x+33=0$, then $x=-33/2$

∴ Breadth (b)$=16m$.

Length (l)$=(2x+1)=2\left(16\right)+1=32+1=33m$

∴ Length (l)$=33m$

Breadth (b)$=16m$.