Triangle ABC is a right-angled triangle.


Its leg AB is   = 24 meters long.


Its area is   = 7*12 = 84 square meters.


Triangles ABC and EDC are similar (since they both are right-angled and have common acute angle C).


Hence, their corresponding sides are proportional.


In particular,  EC = k*AC = 24k,  ED = k*AB = 7k,  where "k" is the proportionality coefficient.


Then the area of the triangle EDC is   =  = .


It is half the area of the triangle ABC, i.e.

      =  = 42,   or


      =  = .


Therefore, the proportionality coefficient (the similarity coefficient)

     k =  = .


It implies  EC = k*AC =  =  = 16.971 (approximately).    ANSWER