Find the unknown quantity for the following pairs of similar shapes.

The diagram shows a ladder that is leaning against a wall. Find the length of the ladder.

The diagram shows a bridge that can be lifted to allow ship to pass below. What is the distance $AB$ when the bridge is lifted to the position shown in the diagram? (Note that the bridge divides exactly in half when it lifts open.)

Triangle $FAB$ is congruent to triangle $FED$. Prove that $BFDC$ is a kite.

Mohamed takes a short cut from his home (H) to the bus stop (B) along a footpath (HB). How much further would it be for Mohamed to walk to the bus stop by going from $H$ to corner ($C$) and then from $C$ to $B?$ Give your answer in metres. Take all values correct up to ones place.

A ladder is standing on horizontal ground and rests against a vertical wall. The ladder is $4.5 \mathrm{m}$ and its foot is $1.6 \mathrm{m}$ from the wall. Calculate how far up the wall, the ladder will reach. Give your answer correct to $3$ significant figures.

Calculate the value of $x$ (in $\mathrm{cm}$)

The diagram shows two jugs that are mathematically similar.

Find the value of $x$( in$\mathrm{cm}$) .