Let the other leg = y and the hypotenuse = z 

Then by the Pythagorean theorem:









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:

, , 

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

So



Solve that and get z=25, y= 24

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

Edwin