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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 $65\ m$.