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
2x(c+d)=b therefore
x=b/2(c+d)
therefore length of sides will be
(cb)/2(c+d) and (db)/2(c+d)
therefore area of rectangle
= (cdb^2)/4(c+d)^2
equating the areas
a^2/16=(cdb^2)/4(c+d)^2
a^2/4 =(cdb^2)/(c+d)^2
a/2 =[[(cd)^1/2]b]/(c+d)
a/2 =[[(cd)^1/2](90-a)]/(c+d)
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.