we can write 2 equations
[tex]\begin{gathered} x\times y=92 \\ \end{gathered}[/tex][tex]x+12=y[/tex]where x is the wide and y the long
we can replace y=x+12 from the second equation on the first
[tex]x\times(x+12)=92[/tex]and solve x
[tex]\begin{gathered} x^2+12x=92 \\ x^2+12x-92=0 \end{gathered}[/tex]factor ussing
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a is 1, b is 12 and c -92
replacing
[tex]\begin{gathered} x=\frac{-(12)\pm\sqrt[]{12^2-4(1)(-92)}}{2(1)} \\ \\ x=\frac{-12\pm16\sqrt[]{2}}{2} \\ \\ x=-6\pm8\sqrt[]{2} \end{gathered}[/tex]the two solutions are
[tex]\begin{gathered} x_1=5.31 \\ x_2=-17.31 \end{gathered}[/tex]the solution must be positive because it is a measure
so x=5.31feet
now we can replace the value of x on any equation to solve y(I will replace on the second equation)
[tex]\begin{gathered} x+12=y \\ 5.31+12=y \\ y=17.31 \end{gathered}[/tex]so the measurements are x=5.31 and y=17.31
