The sum of the lengths of the sides of a rectangle is represented by 32 feet. the width of the rectangle measures 9 feet. what is the length of the rectangle

-- A rectangle has 4 sides.

-- Each side has the same length as the side directly across from it.

-- So there are two sides that are both the width of the rectangle,
and another two sides that are both the length of the rectangle.

-- In this particular rectangle, when you add up all four sides,
the sum is 32 feet.

-- The width of the rectangle is 9 feet.  So there are two sides that are
both 9 feet.  When you add those up, you have 18 feet.

-- The REST of the 32 feet belongs to the other two sides.
That much is (32 - 18) = 14 feet.  That's what the other two
sides add up to when you add them.

-- The other two sides are equal.  So each of them is half of 14 = 7 feet .

This rectangle, or the description of it, is slightly weird.
The length of the rectangle is shorter than the width.
But that's OK.  Two sides are 9 feet, and two sides are 7 feet, and
when you add them all up, you get 32 feet, so our solution is correct.
Let them call the sides anything they want to.