points C, D and E are not collinear. CD=10,CE=4, and DE=X. what are 3 possible lengths x can be so that CDE makes a triangle

x could be 9.2, 10 or 10.8.

Explanation:

If the triangle to be formed would be an isosceles, then:

DE = x = 10.

If the triangle is a right angled with CD = 10 as the hypotenuse. Applying Pythagoras theorem, we have:

 =    +

100 = + 16

100 - 16 =

= 84

x =

 = 9.1652

  ≅ 9.2

If the triangle is a right angled with DE = x as the hypotenuse, then:

    =   +

       = 100 + 16

       = 116

x =

   = 10.7703

x = 10.8