$A$ 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 $m$.

Fill in the blanks using the correct word given in brackets:
$(i)$ All circles are $........$ (congruent,similar)
$(ii)$ All squares are $.........$ (similar,congruent)
$(iii)$ All $.........$ triangles are similar. (isosceles,equilateral)
$(iv)$ Two polygons of the same number of sides are similar,if $(a)$ their corresponding angles are $......$ and $(b)$ their corresponding sides are $......$ (equal,proportional)

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.

An aeroplane leaves an airport and flies due north at a speed of $1000\, km/h$. At the same time,another aeroplane leaves the same airport and flies due west at a speed of $1200\, km/h$. How far apart will be the two planes after $1 \frac{1}{2}$ hours?

State whether the following quadrilaterals are similar or not.

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid-point of $BC$. The ratio of the areas of triangles $ABC$ and $BDE$ is