In a triangle ABC, p and q are points on AC and AB respectively such that PC/AC =3/4 and BQ = 4.5 am. find AQ

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Please find below the solution to the asked query:

Given : In a triangle ABC, P and Q are points on AC and AB respectively such that $\frac{\mathrm{PC}}{\mathrm{AC}} =\frac{3}{4}$  and BQ = 4.5 am. 
Here we assume PQ | | BC as without that information we can't solve given query .

Now from converse of BPT we get

$$\begin{gathered} \frac{\mathrm{PC}}{\mathrm{AP}} = \frac{\mathrm{BQ}}{\mathrm{AQ}} \\ \Rightarrow \frac{\mathrm{PC}}{\mathrm{AC} - \mathrm{PC}} = \frac{\mathrm{BQ}}{\mathrm{AQ}} \\ \Rightarrow \frac{3}{4 - 1} = \frac{4.5}{\mathrm{AQ}} \\ \Rightarrow \frac{3}{1} = \frac{4.5}{\mathrm{AQ}} \\ \Rightarrow \mathrm{AQ} = \frac{4.5}{3} \\ \mathbf{\Rightarrow }\mathbf{AQ}\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{cm}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

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