Question 679676
Pythagorean theorem: {{{a^2 + b^2 = c^2}}}, with c the hypotenuse.

{{{a = c-10}}}
{{{b = c- 80}}}

{{{(c-10)^2 + (c-80)^2 = c^2}}}

{{{c^2 - 20c + 100 + c^2 - 160c + 6400 = c^2}}}

{{{c^2 - 180c + 6500 = 0}}}

{{{(c-50)(c-130) = 0}}}

{{{c-50=0}}} or {{{c-130=0}}}
{{{c=50}}} or {{{c=130}}}

If {{{c=50}}}, then {{{a=c-10=40}}} and {{{b=c-80=-30}}}. We cannot have negative numbers for side length.

Thus:

{{{c=130}}}
{{{a=120}}}
{{{b=50}}}