Question

The area of a rectangular plot is 528 $m^2$. The length of the plot (in meters) is one metre more then twice its breadth. The perimeter of the plot in m is

Answer 1

Let the length of the rectangular plot be $lm$ and the breadth of rectangular plot be $bm$

Area of the rectangular plot $=528m^2$

Hence length of the plot is one metre more than twice its breadth so the equation formed from this statement

$l=2b+1$

Area of rectangular plot $=528$

$\Rightarrow l\times b=528$

$\Rightarrow (2b+1)b=528$ [From $l=2b+1$]

$\Rightarrow 2b^2+b=528$

$\Rightarrow 2b^2+b-528=0$

$\Rightarrow 2b^2+33b-32b-528=0$

$\Rightarrow b(2b+33)-16(2b+33)=0$

$\Rightarrow (2b+33)(b-16)=0$

Breadth of the rectangular plot cannot be negative

So the $b-16=0$

$\Rightarrow b=16m$

Breadth $+16m$

Length of the rectangular plot $\left(l\right)=2b+1$

$=2\times 16+1$

$32+1$

$33m$

Perimeter of the rectangular plot $=2(l+b)=2(33+16)m=2\left(49\right)m=98m$