Let me solve one else will be done similarly
let us divide thread in a and b
such that a+b=90cm
area of square with side a=(a^2)/16
Now we may calculate area of rectangle.
Lea the side of rectangle be in c:d then
therefore length of sides will be
(cb)/2(c+d) and (db)/2(c+d)
therefore area of rectangle
equating the areas
now put any value of c and d and get desired value of a.
e.g if c=4 and d=1 you will get
a=40 and b=50 you will get different answers for different value of c and d
this solution is a general solution. This happend because a number of rectangles are possible for a given parameter.