Question 873259
If the length is 17m and width is 7m,

Let:

x- be the width of the pathway.

Therefore,

17+x    - be the length
7+x     - be the width

The area now will be {{{200 m^2}}} right?

So:

{{{A=lw}}}
{{{200=(17+x)(7+x)}}}
{{{200=119+17x+7x+x^2}}}
{{{200=119+24x+x^2}}}
{{{81=14x+x^2}}}
{{{x^2+24x-81=0}}}
{{{(x-3)(x+27)}}}

Therefore
{{{x=3}}} or {{{x=-27}}}

Since we don't accept negative widths the answer is 3m! Hope that helps!

Steffy