15. Triangle $P Q R$ has been divided into twenty-five congruent right-angled triangles, as shown. The length of $R P$ is $2.4 \mathrm{~cm}$. What is the length of $P Q$ ?
A $3 \mathrm{~cm}$
B $3.2 \mathrm{~cm}$
C $3.6 \mathrm{~cm}$
D $4 \mathrm{~cm}$
E $4.8 \mathrm{~cm}$
15. A The diagrams show one of the twenty-five congruent right-angled triangles and the two such triangles at vertex $\mathrm{R}$.
Let the two acute angles in each of the triangles be $x^{\circ}$ and $y^{\circ}$.

Note that $x+y+90=180$, as the interior angles of a triangle sum to $180^{\circ}$.
So $x+y=90$. In the second diagram, the two angles which meet at $\mathrm{R}$ are $x^{\circ}$ and $y^{\circ}$, so we can deduce that angle $Q R P$ is a right angle.
Let the length of the hypotenuse of each small triangle be $a \mathrm{~cm}$.
Note that angle $Q R P$ is a right angle, $P R$ has length $4 a \mathrm{~cm}$ and $R Q$ has length $3 a \mathrm{~cm}$.
So the lengths of the sides in triangle $P Q R$ are in the ratio $3: 4: 5$.
Therefore the length of $P Q$, in $\mathrm{cm}$, is $5 \times \frac{2.4}{4}=3$.