Question

For a given set of rectangles, the length varies inversely with the width. In one of these rectangles, the length is 75 and the width is 2. For this set of rectangles, calculate the width of a rectangle whose length is 5.

Answer 1

`W=30`

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
`y=(k)/(x)` represents the relation where y is inversely proportional to x and k is the constant of proportionality.

So our required equation would be
`L=(k)/(W)`.

We are told told that the length is 75 and the width is 2.

Upon substituting these values in our equation, we will get:

`75=(k)/(2)`

`k=75\cdot 2=150`

Since constant of proportionality is 150, so our equation would be
`L=(150)/(W)`.

To find the width of the rectangle with length of 5, we will substitute
`L=5` in our equation as:

`5=(150)/(W)`

`W=(150)/(5)`

`W=30`

Therefore, the width of the rectangle would be 30.