Question-218890

Question Number 218890 by Spillover last updated on 17/Apr/25

Answered by mr W last updated on 17/Apr/25

(1/1)×((BF)/(FD))×(3/4)=1 ⇒((BF)/(FD))=(4/3) ⇒Δ_(ADF) =(3/7)×Δ_(ADB) =(3/7)×((3×3)/2)=((27)/(14)) [CDFE]=Δ_(ACF) −Δ_(ADF) =(1/2)×((4×3)/2)−((27)/(14))=((15)/(14)) ✓

$$\frac{\mathrm{1}}{\mathrm{1}}×\frac{{BF}}{{FD}}×\frac{\mathrm{3}}{\mathrm{4}}=\mathrm{1}\:\Rightarrow\frac{{BF}}{{FD}}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\Rightarrow\Delta_{{ADF}} =\frac{\mathrm{3}}{\mathrm{7}}×\Delta_{{ADB}} =\frac{\mathrm{3}}{\mathrm{7}}×\frac{\mathrm{3}×\mathrm{3}}{\mathrm{2}}=\frac{\mathrm{27}}{\mathrm{14}} \\ $$$$\left[{CDFE}\right]=\Delta_{{ACF}} −\Delta_{{ADF}} \\ $$$$\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{4}×\mathrm{3}}{\mathrm{2}}−\frac{\mathrm{27}}{\mathrm{14}}=\frac{\mathrm{15}}{\mathrm{14}}\:\checkmark \\ $$

Commented by Spillover last updated on 17/Apr/25