Question

John is building a fence for the animals on his farm. The perimeter of the rectangle should be less than 100 meters. The length of the rectangle is 4 meters more than the width. Which inequality expresses all of the possible widths, in meters, of the rectangle?

Answer 1

`w<23`

Explanation:

Let l be the length and w be the width of the rectangle

Given:

The length of the rectangle is 4 meters more than the width.

The length of the rectangle is

`l = 4 + width = 4+w`

The perimeter of the rectangle should be less than 100 meters.

The perimeter of the rectangle is
`2(l+w)` and it is less than 100 m.

So, the equation is.

`2(l+w)<100`

Put length of the rectangle in above equation.

`2((4+w)+w)<100`

`2(4+2w)<100`

`8+4w<100`

`4w<100-8`

`4w<92`

`w<(92)/(4)`

`w<23`

Therefore, the inequality expresses all of the possible widths is
`w<23`