In the given figure, $△\mathrm{ABC}~△\mathrm{PQR}$. Find the value of x.

As we know, two triangles are similar if

1. their corresponding angles are equal and
2. their corresponding sides are in the same ratio.

$\because △\mathrm{ABC}~△\mathrm{PQR}$   [Given]

$\therefore \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}=\frac{\mathrm{AC}}{\mathrm{PR}}$

$\Rightarrow \frac{6}{4.5}=\frac{4}{x}=\frac{5}{3.75}$

$\Rightarrow x=\frac{4.5\times 4}{6}$

$\Rightarrow x=3 \mathrm{cm}$