Ok think about it this way.

So all the individual areas add up to the grand total area of

Now you have work out the area of each individual area

We know thatArea 1 will be self service. Its length will be twice its width.

So in this case

Area 2 will be table service. Its width will be 2m more than the width of Area 1 but its length will be half the length of Area 1

Area 3 will be academic staff only. Its width will be 1m more than the width of Area 2 and its length will be 1m more than the length of Area 1

Now sub all those individual equations back into equation 1 and solve for w

I leave you to do the rest. You have to expand then either factorise or use the quadratic formula