In the given figure, ∆ACB ∼ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.
It is given that $\triangle A C B \sim \triangle A P Q$.
$B C=8 \mathrm{~cm}, P Q=4 \mathrm{~cm}, B A=6.5 \mathrm{~cm}$ and $A P=2.8 \mathrm{~cm}$
We have to find $C A$ and $A Q$.
Since $\triangle A C B \sim \triangle A P Q$
$\Rightarrow \frac{B A}{A Q}=\frac{C A}{A P}=\frac{B C}{P Q}$
So
$\frac{6.5 \mathrm{~cm}}{A Q}=\frac{8 \mathrm{~cm}}{4 \mathrm{~cm}}$
$A Q=\frac{6.5 \mathrm{~cm} \times 4 \mathrm{~cm}}{8 \mathrm{~cm}}$
$=3.25 \mathrm{~cm}$
Similarly
$\frac{C A}{A P}=\frac{B C}{P Q}$
$\frac{C A}{2.8 \mathrm{~cm}}=\frac{8 \mathrm{~cm}}{4 \mathrm{~cm}}$
$C A=2.8 \mathrm{~cm} \times 2 \mathrm{~cm}$
$=5.6 \mathrm{~cm}$
Hence, $C A=5.6 \mathrm{~cm}$ and $A Q=3.25 \mathrm{~cm}$