Question

Select the correct answer. A rectangular sheet of steel is being cut so that the length is four times the width. The perimeter of the sheet must be less than 100 inches. length (0) width (w) Which inequality can be used to find all possible lengths, I, of the steel sheet? 201 100 Rese Submit

Answer 1

We have a rectangular sheet with length (l) and width (w)

It is also given that length is four times the width,

`\begin{gathered} l=4w \\ w=(l)/(4) \end{gathered}`

The perimeter of the sheet must be less than 100 inches,

`p<100\:`

Recall that the perimeter of a rectangular shape is given by

`p=2(l+w)`

Substitute it into the above inequality

`2(l+w)<100_{}`

Now substitute the value of w into the above inequality.

`2(l+(l)/(4))<100`

Now let us simplify the above inequality

`\begin{gathered} 2(l+(l)/(4))<100 \\ 2((4l+l)/(4))<100 \\ 2((5l)/(4))<100 \\ (5l)/(2)<100 \end{gathered}`

Therefore, the possible lengths of the rectangular sheet are given by the inequality

`(5l)/(2)<100`

The 2nd option is the correct answer.