Let the width of the table be denoted as \( w \). Then, since the table is four times as long as it is wide, the length \( l \) can be expressed as:
\[ l = 4w \]
According to the problem, if the table were 6 feet shorter in length and 6 feet wider, it would become a square. This can be expressed with the equation:
\[ l - 6 = w + 6 \]
Now, substituting the expression for length \( l \):
\[ 4w - 6 = w + 6 \]
To solve for \( w \), first, rearrange the equation:
\[ 4w - w = 6 + 6 \]
This simplifies to:
\[ 3w = 12 \]
Now, divide both sides by 3:
\[ w = 4 \]
Now that we have the width, we can find the length:
\[ l = 4w = 4 \times 4 = 16 \]
Therefore, the dimensions of the table are:
- Width: \( 4 \) ft
- Length: \( 16 \) ft
To verify, if the length is reduced by 6 ft and the width is increased by 6 ft:
- New Length: \( 16 - 6 = 10 \) ft
- New Width: \( 4 + 6 = 10 \) ft
Since the new dimensions are equal, the table indeed would be square in this scenario.
Thus, the dimensions of the table are:
- Length: 16 ft
- Width: 4 ft