Question 144667
Length of one leg: {{{a}}}


Length of the other leg: {{{b}}}


Assume {{{b}}} is the long leg, so {{{b = 2a + 2}}} (2 more than twice the shorter)


Sum of the lengths of the legs: {{{a + b = 17}}}, but since {{{b=2a+2}}}, {{{a+2a+2=17}}} by substitution.


Collect like terms and solve for {{{a}}}, {{{3a+2=17}}} => {{{3a=15}}} => {{{a=5}}}


So:  {{{5 + b = 17}}} => {{{b=12}}}


Check:
{{{5^2+12^2=25+144=169=13^2}}} Checks.


Note that if we had assumed in the beginning that {{{a}}} was the longer leg, the result would have been that {{{a=12}}} and {{{b=5}}} -- same answer for all practical purposes.