Trapezium Cut Along a Diagonal Into Triangles With Areas in a Givem Ratio

Suppose we have a trapezium cut into two triangles along the diagonal. The top and bottom sides are given in terms of  
  and the height is 4.

The area of BCD is three times the area of ABC. The height of both triangles is 4.
\[\frac{1}{2} (x+4) \times 4=3 \times \frac{1}{2} x \times 4\]


\[4x=8 \rightarrow x=2\]