(c) x = √(1^2 +(√10)^2) = √11
(d) 3^2 = (3x)^2 +(4x)^2 = (9 +16)x^2 . . . . Pythagorean theorem
.. x^2 = 9/25 . . . . . . . . . . . . . . . . . . . . . . . . divide by the coefficient of x^2
.. x = √(9/25) = 3/5
You might recognize that the legs are in the ratio 3:4, so the triangle is a "3-4-5" triangle. The actual hypotenuse is 3, so is 3/5 of 5. Thus, the other two sides are 3/5 of 3 and 3/5 of 4. That means x=3/5.