Answer: 14 in x 14 in x 14 in
Step-by-step explanation:
Given: A block of wood is a cube whose side is x in. long.
Then according to the question, the dimensions of the remaining block be x, x-1,x-3
Then volume of the remaining block is given by:-
[tex]x(x-1)(x-3)=2002\\\Rightarrow\ x^3-4x^2+3x-2002=0[/tex]
By rational root theorem, the possible zeroes are=[tex]\frac{p}{q}[/tex]
Now, here p=2002 and q=1
Then the possible zeroes are factors of 2002,
Now, the factors of 2002=[tex]1,2,7,11,13,14,143,77,22,91,....[/tex]
When we check the above values in the equation, only x=14 satisfy the equation.
Such that [tex]14(14-1)(14-3)=2002[/tex]
hence, the dimensions of the original block of wood= 14 in x 14 in x 14 in
