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Represent the following situations in the form of quadratic equations:The area of a rectangular plot is $528\ m^{2}$. The length of the plot $( in\ metres)$ is one more than twice its breadth. We need to find the leagth and breadth of the plot.
Given: The area of a rectangular plot is $528\ m^{2}$. The length of the plot $( in\ metres)$ is one more than twice its breadth. We need to find the leagth and breadth of the plot.
To do: To represent the given situations in the form of quadratic equations
Solution:
Let the breadth$=b\ m$
$\therefore$ Length$=l=( 2b+1)\ m$
Area$=528\ m^2$ [Given]
$\Rightarrow l\times b=528$
$\Rightarrow ( 2b+1)b-528=0$
$\Rightarrow 2b²+b-528=0$
$\Rightarrow 2b²+33b-32b-528=0$
$\Rightarrow b( 2b+33)- 16(2b+33)=0$
$\Rightarrow ( 2b+33)(b-16)=0$
$\Rightarrow 2b+33=0$ or $b-16=0$
$\Rightarrow b=-\frac{33}{2}$ or $b=16$
$b$ can't be negative, therefore we reject the value $b=-\frac{33}{2}$.
$\therefore b-16=0$
$b=16$
Therefore, breadth$=16\ m$
length$=l=2b+1=2\times16+1=32+1=33\ m$
Updated on: 10-Oct-2022
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