With the rectangle of area $768$ sq m and length $:$ breadth $= 3 : 1$, the side of the square having same perimeter is —

Let breadth $=x$, length $=3x$, so $3x^2=768$ gives $x=16$, making length $48$ m and breadth $16$ m. The rectangle's perimeter is $2(48+16)=128$ m, so the equal-perimeter square has side $128\div4=32$ m.