Triangle ABC is similar to triangle PQR with area(ABC) : area(PQR) = 4 : 9, and the two areas add up to $91{\text{cm}}^2$.
Find area(PQR) in ${\text{cm}}^2$.

Let the areas be 4$k$ and 9$k$. Then $4k+9k=13k=91$, so $k=7$ and area(PQR) = $9\times 7=63{\text{cm}}^2$. The option $28{\text{cm}}^2$ is area(ABC), the other triangle; 54.6 comes from splitting 91 in the side ratio 2 : 3 instead of the area ratio 4 : 9, and 45.5 is simply half of 91.