Area of tiled portion or room = 10(25) = 250 m^2..........ANS
Area of the entire room = (2w+25)(2w+10)
.......................................... 4w^2 + 20w + 50w + 250
.......................................... 4w^2 + 70w + 250..................ANS
Area of the wood frame = 2(25w) + 2(10w) + 4(w^2)
.......................................... 4w^2 + 70w
Owners can only afford 74 m^2 of wood so
4w^2 + 70w = 74
4w^2 + 70w - 74 = 0
...........-70 ±√(70^2 - 4(4)(-74))
w = -----------------------------------
...........................2(4)
...........-70 ± 78
w = ----------------
.................8
w = 1, or -18.5 but you can't have a negative length so the answer is simply
w = 1......................................A...