Question 1132719
Square {{{MNOP }}} has a diagonal of {{{d=12in}}}. 

if the side of square is {{{a}}}, and diagonal cuts the square in two right triangles, using right triangle we have

{{{d^2=a^2+a^2}}}

{{{d^2=2a^2}}}

{{{a^2=d^2/2}}}...........plug in {{{d}}}

 {{{a^2=(12in)^2/2}}}

{{{a^2=144in^2/2}}}

{{{a^2=72in^2}}}

{{{a=sqrt(72in^2)}}}

{{{a=6sqrt(2)in}}}-> exact solution-the length of each side of the square

{{{a=8.49in)}}}->approximately