# Problem of the Week Problem D Find the Largest Area

Rectangle $$ACEG$$ has $$B$$ on $$AC$$ and $$F$$ on $$EG$$ such that $$BF$$ is parallel to $$CE$$. Also, $$D$$ is on $$CE$$ and $$H$$ is on $$AG$$ such that $$HD$$ is parallel to $$AC$$, and $$BF$$ intersects $$HD$$ at $$J$$. The area of rectangle $$ABJH$$ is $$6\text{ cm}^2$$ and the area of rectangle $$JDEF$$ is $$15\text{ cm}^2$$.

If the dimensions of rectangles $$ABJH$$ and $$JDEF$$, in centimetres, are integers, then determine the largest possible area of rectangle $$ACEG$$. Note that the diagram is just an illustration and is not intended to be to scale.