Corresponding sides of two similar triangles are in the ratio $4:9$. Areas of these triangles are in the ratio

It is given that $△ABC~△PQR$ and $\frac{BC}{QR}=\frac{2}{3}$ then $\frac{ar\left(△PQR\right)}{ar\left(△ABC\right)}=$?

Choose the correct answer in each of the following questions:

In an equilateral $△ABC, D$ is the midpoint of $AB$ and $E$ is the midpoint of $AC$. Then, $ar\left(△ABC\right) : ar\left(△ADE\right)=$?

In $△ABC$ and $△DEF$, we have $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{5}{7}$, then $ar\left(△ABC\right) : ar\left(△DEF\right)=$?

Two isosceles triangles have their corresponding angles equal and their areas are in the ratio $25:36$. The ratio of their corresponding height is

The line segments joining the midpoints of the sides of a triangle form four triangles, each of which is

If $△ABC~△QRP, \frac{ar\left(△ABC\right)}{ar\left(△QRP\right)}=\frac{9}{4}, AB=18 \mathrm{cm}$ and $BC=15 \mathrm{cm}$ then $PR=$?

Choose the correct answer in each of the following questions:

In the given figure, $O$ is the point of intersection of two chords $AB$ and $CD$ such that $OB=OD$ and $\angle AOC=45°$. Then, $△OAC$ and $△ODB$ are