Question 863747
{{{3/5}}} of the rectangular yard is the central grass area.


{{{(40-2x)(50-2x)=(3/5)(40*50)}}} using x as the width of the flower border.
{{{(40-2x)(50-2x)=3*40*10}}}
{{{4(20-x)(25-x)=3*40*10}}}
{{{(20-x)(25-x)=300}}}
{{{500-45x+x^2=300}}}
{{{x^2-45x+200=0}}}
discrim, 45^2-4*200=2025-800=1225=49*25
{{{x=(45-sqrt(49*25))/2}}} because the positive sqrt form will not make sense.
{{{x=(45-35)/2}}}
{{{x=10/2}}}
{{{x=5}}}
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Dimensions of the grass area are 40-2*5 by 50-2*5;
or 30 by 40 square yards.
Perimeter of this grass area is {{{highlight_green(3(30+40)=highlight(210))}}} yards.