Question 938606
<pre>
Let the other leg = y and the hypotenuse = z 

Then by the Pythagorean theorem:

{{{7^2+y^2=z^2}}}

{{{49+y^2=z^2}}}

{{{49=z^2-y^2}}}

{{{49=(z-y)(z+y)}}}

That expresses 49 as the product of two positive integers
with z-y less than z+y 

49 can be written as the product of two positive integers
in only 3 ways:

{{{49=1*49}}}, {{{49=7*7}}}, {{{49=49*1}}}

but only the first way has the first factor smaller than the second.

So

{{{system(z-y=1,z+y=49)}}}

Solve that and get z=25, y= 24

So the right triangle has legs 7, 24, and hypotenuse 25. 

Edwin</pre>