Question 703613
Draw that exactly as you describe.  There will be a point on line AB toward the right, and on the line DE downward at which lines AB and DE intersect.  Call this point, R.  You now have a triangle ARE  (using the points, A, R, and E) and it is a Right triangle with angle at R being 90 degrees.  


See that length AR is 8+16, and length ER is 12+6.  


The length AE is the hypotenuse of this triangle.  Use Pythagorean Theorem.

{{{AE^2=AR^2+ER^2}}}, and find AE.
AR = 24, and ER = 18


{{{drawing(300,300,0,26,0,20,
        line(1,1,9,1),
        line(9,1,9,7),
        line(9,7,25,7),
        line(25,7,25,19),
        locate(25,1,R),
      locate(.2,1.8,A),
      locate(9.5,1,B),
      locate(8.1,8,C),
      locate(25.5,7,D),
      locate(24,20,E),
    green( line(9,1,25,1)),
    green( line(25,1,25,7)),
    red( line(1,1,25,19)),
      locate(19,3,Right Angle)
)}}}