8. As shown in the diagram, $F G H I$ is a trapezium with side $G F$ parallel to $H I$. The lengths of $F G$ and $H I$ are 50 and 20 respectively. The point $J$ is on the side $F G$ such that the segment $I J$ divides the trapezium into two parts of equal area. What is the length of $F J$ ?
A 25
B 30
C 35
D 40
E 45
8. C Let $x$ be the length $F J$, and $h$ be the height of the trapezium. Then the area of triangle $F J I$ is $\frac{1}{2} x h$ and the area of trapezium $F G H I$ is $\frac{1}{2} h(20+50)=35 h$. The triangle is half the area of the trapezium, so $\frac{1}{2} x h=\frac{1}{2} \times 35 h$, so $x=35$.