An civil designer plans a roof shaped like a triangle named \(ABC\). In which a support beam \(DE\) is placed parallel to the base \(BC\). Given that \(AD=x^{2}m\), \(BD=21m\), \(AE=2x\ m\), \(EC=3 m\).
Answer the following question:
(i) Which concept is used to find the value of \(x\).
(ii) Find the value of \(x\).
(iii) Determine the lengths of \(AB\) and \(AC\).
(iv) If the height and base of the roof is \(20 m \) and \(10m\) respectively, then find the area of \(\Delta ABC\).