Find the length and height of a bookshelf, with the amount of lumber available is provided

Question

A bookcase is to be constructed, the height of the bookcase is 4 feet longer than the length of a shelf. If 18 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.

Answer 1

Let w = length of a shelf.  Then h  =  w + 4  where his the height of a bookcase

 

We have  2(w+4) + w  =18  for a bookcase with one shelf  So

 

2(w+4)  + w  = 18  or 2w + 8  + w  = 18  so 3w  =  10 or w  = 10/3  3  1/3 feet or 3 feet 4  inches

 

If you were to have 2 shelves then

 

2(w+4)  + 2w  =18  or  2w +8 + 2w  = 18  or

 

4w + 8  =  18  4w  = 10  or w  =  2 1/2 feet  With 3 shelves w  =  2feet

 

Check 3(2)  +  2 (2+4)  =18  The answer depends on how many shelves you assume