To find the width of a rectangle given its length and area, you can use the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Width} \]
In this case, you are given:
- Length = \( \frac{6}{7} \) feet
- Area = 5 square feet
Let \( W \) represent the width of the rectangle. We can rearrange the area formula to solve for the width:
\[ W = \frac{\text{Area}}{\text{Length}} \]
Substituting the values we have:
\[ W = \frac{5 \text{ square feet}}{\frac{6}{7} \text{ feet}} \]
To divide by a fraction, you multiply by its reciprocal:
\[ W = 5 \text{ square feet} \times \frac{7}{6} \text{ feet}^{-1} \]
Calculating this gives:
\[ W = \frac{5 \times 7}{6} = \frac{35}{6} \]
Thus,
\[ W = \frac{35}{6} \text{ feet} \]
Converting \( \frac{35}{6} \) to a mixed number, we find that:
\[ \frac{35}{6} = 5 \frac{5}{6} \]
Therefore, the width of the rectangle is
\[ \frac{35}{6} \text{ feet} \quad \text{or} \quad 5 \frac{5}{6} \text{ feet}. \]