Your answer of 1) is :
square 10cm by 10 cm
rectangle 20 cm by 5cm
well if you see co-incidently I have given this solution.
In my example I took ratio of rectangle sides 1:4 and got
a=40 where a is perimeter of square so one side will be 40/4=10 cm therefore area =10 cm by 10 cm
b=50 where b is perimeter of rectangle since sides are in 1:4 therefore sides of different length will be 20cm and 5 cm therefore area will be 20cm by 5 cm

but answer will vary if ratio is changed like if it is taken 1:9.
So there are many solutions.

hope this explaination helped you