UKMT Senior Mathematical Challenge, 2021

The diagram shows two overlapping triangles: triangle $FGH$ with interior angles $60^\circ$, $30^\circ$ and $90^\circ$ and triangle $EGH$ which is a right-angled isosceles triangle. What is the ratio of the area of triangle $IFG$ to the area of triangle $IEH$?

(A) $1 : 1$ (B) $1 : \sqrt{2}$ (C) $1 : \sqrt{3}$ (D) $1 : 2$ (E) $1 : 3$