Question 867116
"If the rectanggular of the room", means what?  I will use this to mean "a rectangular room".


w and L width and length.
L/w=2, "twice as long as it is wide".
L=2w.
Dimensions of original rectangle are w and 2w.

Partition the room into dimension w and the lengths  of each rectangle part is x and y, so that x+y=L.  This means, x+y=2w.  "Solving" this for y, find y=2w-x.  What now is these two rectangles separated by a partition?


One rectangle part is dimensions w by x.
Other rectangle part is dimensions w by 2w-x.
Either wx=560 OR w(2w-x)=560.  NOT both.  
You seem to have enough information for 1 equation but you have 2 unknown variables.