Question

In the adjacent figure, $△ACB\sim △APQ$. If $BC=8cm$, $PQ=4cm,BA=6.5cm$ and $AP=2.8cm$, find $CA$ and $AQ.$

Answer 1

Given $△ACB\sim △APQ$
$$\begin{array}{cc}& \frac{AC}{AP}=\frac{BC}{PQ}=\frac{AB}{AQ}\\ & \frac{AC}{2.8}=\frac{8}{4}=\frac{6.5}{AQ}\end{array}$$
Consider $\frac{AC}{2.8}=\frac{8}{4}$
$$\begin{array}{cc}& 4AC=8\times 2.8\\ & AC=\frac{8\times 2.8}{4}=5.6cm\end{array}$$
Consider $\frac{8}{4}=\frac{6.5}{AQ}$
$$\begin{array}{cc}& 8AQ=4\times 6.5\\ & AQ=\frac{4\times 6.5}{8}=3.25cm\end{array}$$
Length of $AC=5.6cm$, Length of $AQ=3.25cm$