Let the sides of the two squares be x m and y m. Therefore, their perimeter will be 4x and 4y respectively and their areas will be x2 and y2 respectively. It is given that
4x - 4y = 24
x - y = 6
x = y + 6
Also,x2+y2=468
⇒(6+y)2+y2=468
⇒36+y2+12y+y2=468
⇒2y2+12y+432=0
⇒y2+6y−216=0
⇒y2+18y−12y−216=0
⇒y(y+18)−12(y+18)=0
⇒(y+18)(y−12)=0
⇒y=−18,12
However, side of a square cannot be negative. Hence, the sides of the squares are 12 m and (12 + 6) m = 18 m.