the answer is 3 m
but the method is not known...
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Area of the rectangular garden = l*b
=40*30
=1200m^2
Area of garden with outer part =(40+x)(30+x)
=1200+x^2+70x
Area of path=456m^2
1200+70x+x^2-1200=456
x^2+70x=456
x^2+70x-456=0
x=-70+-√4900+4*456/2
=3
so the width is three
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