Question 734636
{{{x}}}= length of the smaller side
{{{y}}}= length of the longer side
 
Applying the Pythagorean theorem:
{{{x^2+y^2=(3sqrt(10))^2}}} --> {{{x^2+y^2=3^2*(sqrt(10))^2}}} --> {{{x^2+y^2=9*10}}} --> {{{x^2+y^2=90}}}
 
{{{3x}}}= length of the tripled smaller side
{{{2y}}}= length of the doubled longer side
 
Applying the Pythagorean theorem:
{{{(3x)^2+(2y)^2=(9sqrt(5))^2}}} --> {{{9x^2+4y^2=9^2*(sqrt(5))^2}}} --> {{{9x^2+4y^2=81*5}}} --> {{{9x^2+4y^2=405}}}
 
Now, we have the system of equations (linear in {{{x^2}}} and {{{y^2}}})
{{{system(x^2+y^2=90,9x^2+4y^2=405)}}}
which can be easily solved to find
{{{x^2=9}}} and {{{y^2=81}}}, so {{{highlight(x=3)}}} and {{{highlight(y=9)}}}