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Question
That is the complete problem. I am assuming it would be a cuboid.

It was asking for the largest square piece, but like you said, it could not be square.

Also, I read that a timber is 5" wide or wider.

Is there a solution possible from the added information ?

Thanks again.

Answer
"A circular log is 2 feet in diameter. Determine to the nearest inch, the largest square piece of timber that can be cut from the log."
I assume the sides of the log will be removed to form a cuboid:
https://www.flickr.com/photos/dwread/14379676588/in/photostream/

Consider a cross-section of the log with an inscribed square.
diagonal of square = diameter of circle = 2 ft
By the Pythagorean Theorem, each side of the square is √2 ft.
√2 ft × 12 inches/ft ≅ 17 inches
The largest square piece of timber will be 17 inches by 17 inches.
https://www.flickr.com/photos/dwread/14379676588/
:::::
"Determine number of board feet in the timber if it is 12 feet in length, with no allowances for waste."
Well, I learned something new today: 1 board ft = 144 in³.
12 ft × 12 inches/ft = 144 in
volume of timber = 17×17×144 in³ = 289×144 in³ × 1 board ft/(144 in³) = 289 board ft

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