Question 883090
The perimeter is A + B + C.  We know that C = 17.  Therefore A+B = 40-17, or 23
{{{a^2}}}+{{{b^2}}}={{{c^2}}}
{{{a^2}}}+{{{b^2}}}=289
.
If we *assume* that the sides are whole numbers, the possibilities are combinations that equal 23.  Let's use estimating - try using 10 (since it's easy).  Then we would have
10*10 + 13*13
100 + 169
Too little.
9*9 + 14*14 =
81 + 196
Still too little
8*8 + 15*15
64 + 225
Success!