Question 443094
Recall that {{{a^2 + b^2 = c^2}}}.

We know that {{{c = 29}}} and we know that one of the legs is 1 less than the other. Let's choose a to be 1 less than b.

Then {{{a = b-1}}}

{{{(b-1)^2 + b^2 = 29^2}}}
{{{(b-1)*(b-1) + b^2 = 29^2}}}
{{{b^2 -b -b +1  +b^2 = 29^2}}}
{{{b^2 -2b + 1 +b^2 = 29^2}}}
{{{2b^2 -2b + 1 = 841}}}
{{{2b^2 -2b -840}}}
{{{2*(b^2 -b -420)}}}
{{{2(b+20)(b-21)}}}
So b=-20 or b=21
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But it does not make sense to have a negative length, so the one that makes LOGICAL sense is b =21

If b =21, then a=20 since a = b-1.

So we have (20,21,29) is our triangle.