Answer:
[tex]W=30[/tex]
Step-by-step explanation:
Let L represent length of rectangle and W represent width of the rectangle.
We have been given that for a given set of rectangles, the length varies inversely with the width.
We know that the equation [tex]y=\frac{k}{x}[/tex] represents the relation where y is inversely proportional to x and k is the constant of proportionality.
So our required equation would be [tex]L=\frac{k}{W}[/tex].
We are told told that the length is 75 and the width is 2.
Upon substituting these values in our equation, we will get:
[tex]75=\frac{k}{2}[/tex]
[tex]k=75\cdot 2=150[/tex]
Since constant of proportionality is 150, so our equation would be [tex]L=\frac{150}{W}[/tex].
To find the width of the rectangle with length of 5, we will substitute [tex]L=5[/tex] in our equation as:
[tex]5=\frac{150}{W}[/tex]
[tex]W=\frac{150}{5}[/tex]
[tex]W=30[/tex]
Therefore, the width of the rectangle would be 30.
