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

$E$ and $F$ are points on the sides $PQ$ and $PR$ respectively of a $\Delta PQR$. For the following case,state whether $EF || QR$: $PE = 3.9 \ cm, EQ = 3 \ cm, PF = 3.6 \ cm$ and $FR = 2.4 \ cm$.

State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form.

Two poles of heights $6 \, m$ and $11 \, m$ stand on a plane ground. If the distance between the feet of the poles is $12 \, m$,find the distance between their tops.

$A$ ladder is placed against a wall such that its foot is at a distance of $2.5\, m$ from the wall and its top reaches a window $6\, m$ above the ground. Find the length of the ladder in $m$.

In the figure,two chords $AB$ and $CD$ of a circle intersect each other at point $P$ (when produced) outside the circle. Prove that $\Delta PAC \sim \Delta PDB$.