Question

1. what is the width of a rectangle with a length of \\(\frac{3}{7}\\) ft and an area of \\(2\\) ft\\(^2\\)? write an equation to show your work.

Explanation:

Step1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by the formula \( A = l \times w \), where \( l \) is the length and \( w \) is the width.

Step2: Substitute the known values into the formula

We know that \( A = 2 \, \text{ft}^2 \) and \( l = \frac{3}{7} \, \text{ft} \). Substituting these values into the area formula, we get the equation:
\[
2=\frac{3}{7}\times w
\]

Step3: Solve for \( w \)

To solve for \( w \), we can divide both sides of the equation by \( \frac{3}{7} \) (or multiply both sides by the reciprocal of \( \frac{3}{7} \), which is \( \frac{7}{3} \)):
\[
w = 2\div\frac{3}{7}=2\times\frac{7}{3}=\frac{14}{3}
\]

Answer:

The equation is \( 2=\frac{3}{7}w \) (or \( w = 2\div\frac{3}{7} \)) and the width is \( \frac{14}{3} \, \text{ft} \).