A rectangular garden $50$ m by $40$ m has a path of equal width inside its boundary. If the area excluding the path is $1200$ sq. m, the width of the path is—

With path width $x$, the inner rectangle measures $(50-2x)$ by $(40-2x)$. Setting $(50-2x)(40-2x)=1200$ gives $4x^2-180x+800=0$, i.e. $x^2-45x+200=0$, whose valid root is $x=5$.