IMAS 2023–2024 — Upper Primary — Round 2 Question 8

In triangle $ADE$, points $B,C$ are on $AD$ and $G,F$ are on $AE$ so that $BG\parallel CF\parallel DE$ and the areas of trapezoids $BCFG$ and $CDEF$ are the same, as shown in the diagram below. If $BG:CF=1:5$, what is $AC:BD$?



Answer-entry instruction (editorial): enter the ratio in lowest whole-number terms as a:b.