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Question Number 172918 by mnjuly1970 last updated on 03/Jul/22

Commented by som(math1967) last updated on 03/Jul/22

$$\mathit{y}\mathit{e}\mathit{s}\mathit{i}\mathit{g}\mathit{o}\mathit{t}\frac{16}{3}\mathit{c}\mathit{m}$$

Commented by infinityaction last updated on 03/Jul/22

$$\frac{16}{3}???$$

Commented by som(math1967) last updated on 03/Jul/22

Commented by som(math1967) last updated on 03/Jul/22

$$AE\parallel PQ\parallel \mathit{B}C$$$$△ADQ\sim △ACB$$$$\therefore \frac{DQ}{BC}=\frac{AQ}{AB}=\frac{4}{12}=\frac{1}{3}$$$$\Rightarrow DQ=\frac{1}{3}BC=\frac{8}{3}$$$$PD=\frac{2}{3}AE=\frac{8}{3}$$$$\therefore PQ=\frac{8}{3}+\frac{8}{3}=\frac{16}{3}cm$$

Commented by mnjuly1970 last updated on 03/Jul/22

$$\mathrm{excellent}\mathrm{sir}$$

Commented by Tawa11 last updated on 03/Jul/22

$$\mathrm{Great}\mathrm{sir}$$

Commented by infinityaction last updated on 04/Jul/22

Commented by infinityaction last updated on 04/Jul/22

$$AF=12andEF=8$$$$△ADF\sim APE$$$$\frac{PE}{4}=\frac{4}{12}\Rightarrow PE=\frac{4}{3}$$$$PQ=PE+EQ$$$$PQ=\frac{4}{3}+4=\frac{16}{3}$$

Commented by Tawa11 last updated on 06/Jul/22

$$\mathrm{Great}\mathrm{sir}$$

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