Question 1151596
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The statement of the problem is deficient.  The distance from E to C can't be determined with the given information.<br>
We can use AD as the base of triangle ADE and AB as the base of triangle ABC.  Then we know the ratio of the bases of the two triangles is 2:3.<br>
We can then determine the ratio of the altitudes of the two triangles, knowing that the ratio of the areas is 3:5.<br>
{{{(2/3)(a/b) = 3/5}}}
{{{a/b = 9/10}}}<br>
So the altitude of triangle ADE has to be 9/10 of the altitude of triangle ABC for the ratio of the areas to be 3:5.<br>
But there is no information given that allows us to convert that result into a distance between E and C.<br>