Question 930973
d for diagonal; y and x the sides, y is longer side.


d+y=3x;  y-x=120.
x and y also form two right triangles since x and y form a rectangle.
x^2+y^2=d^2.


System:
{{{system(d+y=3x,y-x=120,x^2+y^2=d^2)}}}
More than one way to go to solve the system, but you are mostly interested in x and y.  The area will be {{{xy}}}.


Try focusing first on eliminating d from the quadratic equation and then eliminate either x or y from the quadratic equation:
{{{d=3x-y}}} from first equation.
{{{x^2+y^2=(3x-y)^2}}} when substituted.
{{{x^2+y^2=9x^2-6xy+y^2}}}
Notice {{{y^2}}} is shown on both sides.
{{{x^2=9x^2-6xy}}}
{{{0=8x^2-6xy}}}
{{{highlight_green(4x^2-3xy=0)}}}
Now, use the second equation of the system to eliminate y in this simplified quadratic equation, and solve for x.