My Gf's professor asked her to solve this problem:
Two square rooms have an area of $52m^2$. The two rooms have a perimeter of 40 meters. Given this, we need to compute the length of the side of the two rooms.
Starting form this: Area of a room=$52\over 2$=$26m^2$.
Since we know that the area of a square is $x^2=26m^2$, we can do $\sqrt{26}$ to find the side of one room, which is 5.099 m.
Since $5.099m * 5.099m$ = $26 m^2$(area of one room) and $5.099 * 4=20.396 m$(perimeter). Both multiplied by 2 gives back: $52 m^2 $ which is the area of the two rooms. $40.792 m$ which is the total perimeter of the two rooms.
Her professor said that the solutions for the area of the two rooms are:
Side First Room: 4,8 meters
Side second Room: 5.2 meters
So were is my mistake?
we have $$a^2+b^2=52$$ and $$4a+4b=40$$ thus we get from equation 2) $$b=10-a$$ and now you can calculate $$a$$ from $$a^2+(10-a)^2=52$$