The length of the room is 96 ft.
Let L be the length of the room and W be the width of the room.
Since the length is twice its width, L = 2W.
Its area A = LW
= 2W × W
= 2W²
If each side were increased by 1 foot, then its new area is A' = (L + 1)(W + 1)
= (2W + 1)(W + 1)
= 2W² + 3W + 1
Since the room would contain 145 ft more if each side were increased by 1 foot, then its new area is A' = A + 145 = 2W² + 3W + 1
2W² + 145 = 2W² + 3W + 1
145 = 3W + 1
3W = 145 - 1
3W = 144
W = 144/3
W = 48 ft.
Since its length L = 2W, substituting W = 48 into the equation, we have
L = 2(48)
L = 96 ft
So, the length of the room is 96 ft.
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