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
flbyrne | (Level 3) Assistant Educator
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 | Student, Undergraduate | (Level 1) Valedictorian
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]