Question Number 215715 by Hanuda354 last updated on 15/Jan/25
Commented by Hanuda354 last updated on 15/Jan/25
$$\mathrm{Find}\:{x} \\ $$
Answered by som(math1967) last updated on 16/Jan/25
![((CF)/(FE))=((CD)/(DE)) [DF is bisector of ∠D] CF=(6/9)×7.2=4.8 now BF∥AE ∴ (x/(7.8))=((4.8)/(7.2)) ⇒x=((4.8×7.8)/(7.2))=5.2 unit](Q215717.png)
$$\:\frac{{CF}}{{FE}}=\frac{{CD}}{{DE}}\:\:\:\left[{DF}\:{is}\:{bisector}\:{of}\:\angle{D}\right] \\ $$$$\:{CF}=\frac{\mathrm{6}}{\mathrm{9}}×\mathrm{7}.\mathrm{2}=\mathrm{4}.\mathrm{8} \\ $$$${now}\:\:{BF}\parallel{AE} \\ $$$$\therefore\:\frac{{x}}{\mathrm{7}.\mathrm{8}}=\frac{\mathrm{4}.\mathrm{8}}{\mathrm{7}.\mathrm{2}}\:\Rightarrow{x}=\frac{\mathrm{4}.\mathrm{8}×\mathrm{7}.\mathrm{8}}{\mathrm{7}.\mathrm{2}}=\mathrm{5}.\mathrm{2}\:{unit} \\ $$
Commented by Hanuda354 last updated on 16/Jan/25
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much},\:\mathrm{sir}. \\ $$