Question

Placing a decorative border around a picture .altogether she uses 18ft of border what could b the possible areas of the picture? Show your work ! and find at least 2 ways

Answer 1

The absolutely positively most area that the picture could possibly have is
25.783 square feet (rounded).  That would happen if the picture is circular
and the 18-ft goes around its circumference.  Then its diameter is 18/pi =
about 5.73 ft and its radius is about 2.865 ft. 

If the picture has straight sides, then its greatest possible area is 20.25 square ft.
That happens if the picture is square and the 18-ft goes around its perimeter.
Then each side is  4.5-ft.

The area can be as small as you want, with no limit.

For example,

-- if the picture is 1-ft high and 7-ft wide, and the 18-ft goes
around its perimeter, then its area is 7 square feet;

-- if the picture is 6-in high and 7-1/2 ft wide, and the 18-ft goes
around its perimeter, then its area is 3.75 square feet;

-- if the picture is 1-in high and 8-ft 11-in wide, and the 18-ft goes
around its perimeter, then its area is 0.743 of a square foot.