Aright triangle has a hypotenuse of length 35. the ratio of the length of the shorter leg to the longer leg of the triangle is 3: 4. what is the length of the shorter leg of the triangle?

As given, 3:4 is the ratio of shorter leg to longer leg. We assume that hypotenuse is 5. It always works that way: 3:4:5, 5 as the hypotenuse. However this is only in right triangles. Ok so 5 is 35. What we need is the 3. Set up a proportion as such:
(3/5)=(x/35). Cross multiply so you get 3*35 which is 105. Divide it by 5. 105/5=21. 21 is your answer.