Question 985630
w, pool width
L, pool length
k, how much longer than wide
u, uniform border width around pool
A, area of the border
-
{{{w=unknown}}}
{{{L=w+k=unknown}}}
{{{k=5}}}
{{{u=2}}}
{{{A=54}}}


{{{wL=poolArea}}}
{{{(w+2u)(L+2u)=totalArea}}}
{{{highlight_green((w+2u)(L+2u)-wL=A)}}}, to relate areas to given border area


First solve for w.
{{{wL+2uL+2uw+4u^2-wL=A}}}
{{{2uL+2uw+4u^2=A}}}
{{{2u(w+k)+2uw=A-4u^2}}}
{{{4uw+2uk=A-4u^2}}}
{{{4uw=A-4u^2-2uk}}}
{{{highlight_green(w=(A-4u^2-2uk)/(4u))}}}


Substitute the known values and evaluate w.
{{{w=(54-4*2^2-2*2*5)/(4*2)}}}
{{{highlight(highlight(w=9/4))}}}


Use w now found, to evaluate L.
{{{L=9/4+5}}}
{{{highlight(highlight(L=29/4))}}}