Question 836017
New area of the lawn becomes {{{(60-2w)(80-2w)=2400}}}, using w as the width of the sidewalk.


{{{4(30-w)(40-w)=4*600}}}
{{{(30-w)(40-w)=600}}}
{{{1200-70w+w^2=600}}}
{{{600-70w+w^2=0}}}


Try to factor the quadratic expression.
600=100*2*3=2*5*2*5*2*3=2*2*2*3*5*5,,,, if seems too much trouble, just use general solution for a quadratic formula.


Discrim, 70^2-4*600=4900-2400=2500
{{{w=(70+- sqrt(2500))/(2)}}}
{{{w=(70+- 5*10)/2}}}, we must use the positive value.
{{{highlight(w=10)}}} or {{{cross(w=60)}}}, only one of them making sense.


Worth a check:
(60-2*10)(80-2*10)=2400?
{{{(60-20)(80-20)}}}
{{{40*60=2400}}} yes.