Question 691493
Let the shorter side = {{{ x }}} then other side = {{{ x + 17 }}}.

Then by Pythagoras, {{{ x^2 + (x + 17)^2 = 25^2 }}}

Multiplying out gives:
{{{ x^2 + (x^2 + 34x + 289) = 625 }}}
{{{ 2x^2 + 34x - 336 = 0 }}}
{{{ x^2 + 17x - 168 = 0 }}}
{{{ (x - 7)(x + 24 ) = 0 }}}
so {{{ x = 7 }}} or {{{ x = -24  }}}

as x represents a side of a triangle then {{{ x > 0 }}} so solution is {{{ x =7 }}}