Question 498614
Let the length of the side of the square be s.
The area of the square is given by:
{{{A = s^2}}} Increase the area by 9 means: {{{9A}}} and we'll show the increase in the length of the side by: {{{n*s}}}, so...
{{{9A = (n*s)^2}}} but {{{A = s^2}}} so we substitute...
{{{9(s^2) = (n*s)^2}}} Simplify and solve for s.
{{{9s^2 = n^2*s^2}}} Divide both sides by {{{s^2}}}
{{{9 = n^2}}} Take the square root.
{{{3 = n}}}
So the sides of the square (s) would increase by 3 times.