Question 880432
w and L, width and length.
{{{L=10+w}}}, for the first part of the description.


Each side is increased by 10 feet.
{{{w+10}}} the increased width;
{{{L+10=10+(w+10)=w+20}}}, the increased length.


The increased dimensions makes area become {{{2wL}}}, the area of the original rectangle multiplied by 2.


Find original w and L.

Original area, {{{wL=w(w+10)=w^2+10w}}}.
Increased area, {{{(w+10)(L+10)=(w+10)(w+20)=w^2+30w+20}}}.


We were given that increased area equals two times the original area:
{{{highlight_green(w^2+30w+20=2(w^2+10w))}}}
{{{w^2+30w+20=2w^2+40w}}}
{{{20=w^2+10w}}}
{{{w^2+10w-20=0}}}
D=100-4*(-20)=100+80=180, sqrt(180)=sqrt(3*6*2*5)=sqrt(3*3*2*2*5)=6sqrt(5).
{{{w=(-10+6sqrt(5))/2}}}
Original width, {{{highlight(w=-5+3sqrt(5))}}}.
{{{L=w+10}}}
{{{L=3sqrt(5)-5+10}}}
Original length, {{{highlight(L=3sqrt(5)+5)}}}.