you want to make a rectangular banner that is 18 feet long you have no more than 48 feet of trim for the banner. what are the possible widths of the banner

Question

you want to make a rectangular banner that is 18 feet long with a trim that goes around the entire border of the banner. you have no more than 48 feet of trim for the banner. what are the possible widths of the banner?

Answer 1

The width of the trim is not given so the width will vary depending on the width of the trim.

The maximum width of the banner occurs if the trim is very narrow, let's say it is a string with zero width as the extreme case.

The length of the banner is 36 and the width is 2x. The perimeter is 36 + 2x which must equal the trim.

36 + 2x = 48

2x = 12

x = 6

x must be less than 6 because the trim can not be zero width.

What happens if the trim gets wider? Let's use 2 inch trim width.

Then the length of the trim for each long side is 18 + 4 = 22. Total length for sides = 44.

The length of the trim for each short side is x. Total length for sides = 2x.

44 + 2x = 48

2x = 4

x = 2

So the width gets smaller as the trim width gets wider.

The maximum width is less than 6 .

The minimum width is zero.

The width must be 0 < width < 6.