Question 155665
The bookshelf is rectangular in shape with {{{Length=3H}}}---> condition 1, 3 times the height
Take note {{{Width=Height=H}}}
Total {{{Perimeter=P=60ft}}}, total feet of lumber available.
So, {{{P=2(L+W)}}} ------------------------> working eqn
but, {{{W=H}}} and {{{L=3H}}}, then:
{{{P=2(3H+H)}}} 
{{{60ft=6H+2H}}}
{{{60ft=8H}}} -----> {{{cross(60)7.5ft/cross(8)=cross(8)H/cross(8)}}}
{{{H=7.5ft}}}
And, {{{L=3*7.5=22.5ft}}}
In doubt? Go back working eqn, remember {{{W=H}}}
{{{60ft=2(22.5+7.5)}}}
{{{60=2(30)}}}
{{{60ft=60ft}}}
Thank you,
Jojo