Question

A rectangular plot has a concrete path running in the middle of the plot parallel to the parallel to the breadth of the plot. The rest of the plot is used as a lawn ,which has an area of 240sq. m. If the width of the path is 3m and the length of the plot is greater than its breadth by 2m ,what is the area of the rectangular plot(in m )?

Answer 1

Let the width be x ma nd length be (x+2)m

Area of path = 3x sq. m

$x(x+2)-3x=240$

$\Rightarrow x^2+2x-3x=240$

$\Rightarrow x^2-x-240=0$

$\Rightarrow x^2-16x+15x-240=0$

$\Rightarrow x(x-16)+15(x-16)=0$

$\Rightarrow x+15=0,x-16=0$

$\therefore x=16$

Length = $16+2=18m$

$\therefore$ Area of the plot = $16\times 18=288$ sq. m