The truss below is designed to support a linearly increasing distributed load between joints B and C$.$ Under this loading, joint C will obviously deflect downward. However, if we intentionally design member DE too long, then joint C will be initially propped upward. Determine how much longer we need to make member DE such that joint C will have zero deflection under load relative to joint A$.$ All members have $A=1\mathrm{.}5i{n}^2$ and $E=10,000$ksi.

$($The deflected shape is shown below if member DE is intentionally too long and no load is applied to the truss.$)$