Call the dimensions of the original rectangle a and b, then we are asked to find ab.
After cutting squares of length 2 from all angles, we'll have the box of the height 2 and the horizontal dimensions of a - 4 and b - 4. This way, the volume...
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Call the dimensions of the original rectangle a and b, then we are asked to find ab.
After cutting squares of length 2 from all angles, we'll have the box of the height 2 and the horizontal dimensions of a - 4 and b - 4. This way, the volume will be `2 ( a - 4 ) ( b - 4 ) ` and it is given to be 72. This gives us one equation, `( a - 4 ) ( b - 4 ) = 36 .`
The second option is to cut 3 units from each angle. The volume will be `3 ( a - 6 ) ( b - 6 ) = 42 , ` which is the second equation.
Opening parentheses in both equations, we get
`ab - 4 ( a + b ) = 20 ` and `ab - 6 ( a + b ) = -22 .`
It may be considered as a linear system for ab and a+b. We can eliminate a+b by adding the first equation multiplied by 6 and the second multiplied by -4:
2ab = 120+88, ab = 104 (square units).