Question 568702
You've got it backwards.
If the length of the side of the picture frame is {{{12}}} inches, the total area of frame plus picture is
{{{12^2}}} square inches = {{{144}}} square inches.
If {{{x}}} inches is the length of the side of the square picture, the area of the square picture is {{{x^2}}} square inches. Since that is 75% of the {{{144}}} square inches of total area,
{{{x^2=0.75*144}}} --> {{{x^2=108}}}
Solving:
{{{x=sqrt(108)}}} --> {{{x=sqrt(4*27)}}} --> {{{x=sqrt(2^2*3^3)}}} --> {{{x=sqrt(2^2)*sqrt(3^3)}}} --> {{{x=sqrt(2^2)*sqrt(3^2*3)}}} --> {{{x=2*sqrt(3^2)*sqrt(3)}}} --> {{{x=2*3*sqrt(3)}}} --> {{{x=6sqrt(3)}}}