Designers want a border's length to be 5 ft greater than its width. A maximum of 180 ft is to be used. Solve an inequality that has possible widths.

2 Answers | Add Yours

flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

Posted on

We have a rectangle with width x ft., so the length is (x+5 ft.). The perimeter, or length of the border is equal to 2x+2(x+5 ft.) and cannot be longer than 180ft. This can be expressed as:

`2x+2(x+5)<=180`

`2x+2x+10<=180`

`4x+10<=180`

`4x<=180-10`

`x<=170/4`

`x<=42.5 ft.`

Thus the width needs to be less than 42.5 ft.

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Designers want a border's length to be 5 ft greater than its width. A maximum of 180 ft is to be used.

If the width of the border is x, the length is x + 5. The length of the border is equal to 2x + 2*(x +5) = 2x + 2x + 10

As this has to be less than or equal to 180

`4x + 10 <= 180`

`4x <= 170`

`x <= 42.5`

The width of the border can be any value in the set (0, 42.5]

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question