Question 1148799
Let x be side length small square
and let y be side length of big square.


This means  {{{system(4x+4y=80,and,y^2=3x^2)}}}.


Simpler system  {{{x+y=20,y^2+3x^2}}}


{{{y=20-x}}}
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{{{y^2=(20-x)^2=400-40x+x^2}}}
-
{{{400-40x+x^2=3x^2}}}
{{{200-20x=x^2}}}
{{{x^2+20x-200=0}}}


{{{x=(-20+sqrt(400+4*200))/2}}}


{{{highlight_green(x=-10+10sqrt(3))}}}, edge length of smaller square;  use it to find y.















-----------------------------------------------------mistake-------------------
Simplified, system is {{{system(x+y=20,and,y^2=3x^2)}}}.

Subst for x and simplify,
{{{y^2-60y+600=0}}}

{{{cross(y=60-10sqrt(3))}}} or {{{cross(y=60+10sqrt(3))}}}
and you can find any corresponding x values.