Question 29806
OK...with questions like these...a diagram is a MUST!


Draw a rectangle (i shall call it ABCD but you do not need to label it) and then a slightly larger one around it (i shall call it KLMN but you do not need to label it).


The outer rectangle, KLMN, is the garden. 
The inner rectangle, ABCD, is the lawn? whatever it is...the Q doesn't say.

The path is the "pathlike" area between the 2 rectangles.


LABELLING
OK, label lengths of KLMN as 20 and 30.
Label the width of the path as x.


So... width of long edge of inner rectangle is 30 less 2 x's --> (30-2x)
and the width of the short edge of inner rectangle is 20 less 2 x's --> (20-2x).


And we know that the area of the inner rectangle is 400. So we have


(30-2x)(20-2x) = 400
{{{ 600 - 60x - 40x + 4x^2 = 400 }}}
{{{ 600 - 100x + 4x^2 = 400 }}}
{{{ 200 - 100x + 4x^2 = 0 }}}
{{{ 4x^2 - 100x + 200 = 0 }}}
{{{ x^2 - 25x + 50 = 0 }}}


solve this to find x.


jon.