Question 881184
The hypotenuse is the longer side of a right triangle.
The other two sides of a right triangle are called legs.
{{{x}}}= length of one of the legs, in mm.
{{{y}}}= length of the other leg, in mm.
 
The perimeter is 90mm gives us the equation
{{{x+y+41=90}}}<--->{{{x+y=90-41}}}<--->{{{x+y=49}}}<--->{{{y=49-x}}}
 
The Pythagorean theorem, applied to this particular triangle, tells us that
{{{x^2+y^2=41^2}}}<--->{{{x^2+y^2=1681}}}
 
{{{system(y=49-x,x^2+y^2=1681)}}}--->{{{system(y=49-x,x^2+(49-x)^2=1681)}}}--->{{{system(y=49-x,x^2+2401-98x+x^2=1681)}}}--->{{{system(y=49-x,2x^2-98x+720=0)}}}--->{{{system(y=49-x,x^2-49x+360=0)}}}
{{{x^2-49x+360=0}}}--->{{{(x-40)(x-9)=0}}}--->{{{system(x=40,"or",x=9)}}}
and those are the lengths (in mm) of the legs of the right triangle, because
{{{system(y=49-x,x=40)}}}--->{{{system(y=9,x=40)}}} and {{{system(y=49-x,x=9)}}}--->{{{system(y=40,x=9)}}} .
Either way, lengths of the other two sides of the right triangle are
{{{highlight(40mm)}}} and {{{highlight(9mm)}}} .