Question 104684
let the height be {{{a}}}, and the length {{{b}}}
The {{{height}}} of a bookcase is {{{3ft}}} longer than the {{{length }}}of a shelf.

so, we can write:
{{{a = b+ 3ft}}} 
or
{{{b= a - 3ft}}}

If 18 feet of lumber is available for  the entire unit, the perimeter is {{{18ft}}}

if perimeter is {{{P}}},

{{{P = 2(a + b)}}}

{{{18ft = 2( a + b - 3ft)}}} we can divide both sides by {{{2}}}, and we will have

{{{9 ft= 2a - 3ft}}}

{{{2a = 9 + 3ft}}}

{{{2a= 12ft}}} divide both sides by {{{2}}}


{{{a = 6ft}}}

then

{{{b = a - 3ft}}}

{{{b= 3ft}}}