Question 805594
Original area, 25*15 square meters.
60% of original area, (0.6)(25)(15).
Let x = width of the strip around the unmowed area.


One side of the unmowed rectangle is 25-2x meters.
The other side of the unmowed rectangle is 15-2x meters.


Area of unmowed region is {{{(25-2x)(15-2x)=(0.6)(25)(15)}}}
{{{(25-2x)(15-2x)=225}}}
{{{375-30x-50x+4x^2=225}}}
{{{4x^2-80x+375-225=0}}}
{{{4x^2-80x+150=0}}}
{{{highlight(2x^2-40x+75=0)}}}


If you do not feel like checking for factorability, use general solution:
{{{x=(40+sqrt(1600-4*2*75))/(2*2)}}}
{{{x=(40+sqrt(1000))/(2*2)}}}
{{{x=(40+100)/4}}}
{{{x=10+25}}}
{{{highlight(x=35)}}} meters