Question

what is the width of a rectangle with a length of \\( \frac { 5 } { 6 } \\) feet and an area of 3 square feet? write an equation to show your work.
choose the correct equation below.
a. \\( 3 w = \frac { 5 } { 6 } \\)
b. \\( \frac { 5 } { 6 } w = 3 \\)
c. \\( w = \frac { 5 } { 6 } \cdot 3 \\)
d. \\( w = \frac { 5 } { 6 } + 3 \\)
what is the width of the rectangle?
\\( \square \\) feet
(type a whole number, fraction, or mixed number.)

Explanation:

Step1: Recall the area formula of a rectangle

The area formula of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width. Given \(l=\frac{5}{6}\) feet and \(A = 3\) square feet. Substituting these values into the formula gives \(\frac{5}{6}\times w=3\).

Step2: Solve the equation for \(w\)

We have the equation \(\frac{5}{6}w = 3\). To solve for \(w\), we use the property of equality. Multiply both sides of the equation by the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\). So \(w=3\times\frac{6}{5}=\frac{18}{5}=3\frac{3}{5}\)

Answer:

B. \(\frac{5}{6}w = 3\)
\(3\frac{3}{5}\) feet