Algebra word problem

[Guest]

Hi,

I would really appreciated some help on this problem:

Q: Grace has a rectangular lawn that is 15m long and 6m wide. The lawn is to be surrounded by a path. The width of the path on each side of the lawn is the same. The area of the path is twice the area of the lawn. Calculate the width of the path.

I calculated the area of the lawn(6x15=90mm^2) and then I doubled it(180m^2). If I make x the width of the path and y and length, then xy=180m^2. I don't know what to do now though. Thanks very much for you help.

[shyamjayakannan]

the path together with the lawn, forms a bigger rectangle. so the area of the path alone will be the difference in the area of the two rectangles. Let the thickness of the path be [tex]x[/tex]. So, the length and breadth of the bigger rectangle will be [tex]15+2x[/tex] and [tex]9+2x[/tex], respectively.

Now, area of the path = [tex](15+2x)(9+2x)-15\times9=4x^2+48x[/tex]

Also since this is double the area of the lawn, [tex]4x^2+48x=2\times15\times9\Rightarrow2x^2+24x-135=0[/tex]

Now you can solve this quadratic for [tex]x[/tex].