Question 901563
x side of the square
w width of the rectangle
L length of the rectangle


{{{x^2+wL=268}}};   {{{w=2+x}}};   {{{L=2+w}}}.


Can a way be found to put the quadratic area equation completely in terms of x?


{{{x^2+(x+2)L=268}}}, using the w linear equation;
{{{x^2+(x+2)(w+2)=268}}}, using the L linear equation;
{{{x^2+(x+2)(2+x+2)=268}}}, again using the w linear equation.


Simplify the quadratic area equation.
{{{x^2+(x+2)(x+4)-268=0}}}
{{{x^2+x^2+6x+8-268=0}}}
{{{2x^2+6x-260=0}}}
{{{x^2+3x-130=0}}}, factorable.
{{{highlight_green((x-10)(x+13)=0)}}}


From that, {{{highlight(x=10)}}}.
w=12 and L=14.