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 a rectangular plot$=528\ m^2$.

The length of the plot (in meters) is one meter more than twice its breadth.

To do:

We have to find the length and breadth of the plot.

Solution:

Let the breadth of the plot be $x\ m$.

This implies,

Length of the plot$=2x+1\ m$.

We know that,

Area of a rectangle of length $l$ and breadth $b$ is $lb$.

Therefore,

Area of the rectangular plot$=(x)(2x+1)\ m^2$.

According to the question,

$x(2x+1)=528$   (From equation 1)

$2x^2+x=528$

$2x^2+x-528=0$

Solving for $x$ by factorization method, we get,

$2x^2+33x-32x-528=0$

$2x(x-32)+33(x-32)=0$

$(2x+33)(x-32)=0$

$2x+33=0$ or $x-32=0$

$2x=-33$ or $x=32$

Length cannot be negative. Therefore, the value of $x=32$.

$2x+1=2(32)+1=64+1=65\ m$

The breadth of the plot is $32\ m$ and the length of the plot is $65\ m$.