The two triangles in the diagram are similar.

There are two possible values of $x$.

Work out each of these values.
State any assumptions you make in your working.

$ABC$ and $AED$ are straight lines.
$BE$ and $CD$ are parallel.

$BE=1.5cm.\;CD=6cm.\;AD=5cm.$

Calculate the length of $ED$.

Triangle $KLM$is similar to triangle $KNJ$.  
$JKM$ and $NKL$are straight lines.

$K\overset{\textasciicircum{}}{L}M=K\overset{\textasciicircum{}}{N}J$ and$L\overset{\textasciicircum{}}{K}M=y^{\circ}$.

$KL=6cm$, $KM=10.5cm$ and $KN=10cm$.
The area of triangle $JKN$ is 75 cm².
Calculate $y.$

$y$= ................................

In the diagram, $PQ$ is parallel to $BC$.
$APB$ and $AQC$ are straight lines.
$PQ$ = 8 cm, $BC$ = 10 cm and $AB$ = 9cm.

Calculate $PB$.

$PB$ = .......................................... cm