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.