Question 805447
Side lengths h, x, y.  
h is for hypotenuse.


Perimeter, {{{h+x+y=1010}}}.
Let one side equal {{{y=293}}}.
Allows for statement, {{{h+x+293=1010}}}.
Simplify a bit: {{{h+x=717}}}.


Pythagorean Theorem lets us say
{{{x^2+y^2=h^2}}}
{{{x^2+293^2=h^2}}}.


System of two equation with unknowns x and h:
{{{x^2+293^2=h^2}}} and {{{h+x=717}}}


Take your pick.  Use the perimeter equation for a formula for either h or x and substitute into the pythagorean equation.   If doing as {{{h=717-x}}}, then make {{{x^2+293^2=(717-x)^2}}}
{{{x^2+293^2=717^2-2*717x+x^2}}}
Note the {{{x^2}}} on both sides.
{{{293^2=717^2-2*x}}}
{{{2x+293^2=717^2}}}
{{{2x=717^2-293^2}}}, DIFFERENCE OF TWO SQUARES,
{{{2x=(717+293)(717-293)}}}
{{{highlight(x=(1/2)(717+293)(717-293))}}}
'
Just compute x and use it to compute h.
Reminder: {{{highlight(h=717-x)}}}