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UKMT Pink Kangaroo, 2017

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

As shown in the diagram, $FGHI$ is a trapezium with side $GF$ parallel to $HI$ . The lengths of $FG$ and $HI$ are 50 and 20 respectively. The point $J$ is on the side $FG$ such that the segment $IJ$ divides the trapezium into two parts of equal area. What is the length of $FJ$ ?

(A) $25$ (B) $30$ (C) $35$ (D) $40$ (E) $45$

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