Since your teacher said to use the Pythagorean you must have been
told they were the sides of a RIGHT triangle, for that's the only
kind of triangle the Pythagorean theorem is true for:

If the legs are 3x and (x+1), and the hypotenuse is (4x-3)² 
then the Pythagorean theorem gives us:


   a² +     b² =      c²

(3x)² + (x+1)² = (4x-3)²

Can you solve that?  If not post again asking how to solve
that equation for x.  There are two solutions for x,

however only one of the two solutions gives all positive values
for the sides of the right triangle when you substitute them
for x in:
 
3x, (x+1) and (4x-3).

Edwin