चित्र में DE||BC और AD:DB = 5:4 है तो `(ar(DeltaDEF))/(ar(DeltaCFB))` ज्ञात कीजिये

Explanation

`thereforeDE"||"BC`
`therefore" "DeltaADE" और "DeltaABC` में
`therefore" " angle5=angle6" "` (संगत कोण)
और `" " angleA=angleA" "` (उभयनिष्ठ)
`therefore" " DeltaADE~DeltaABC" "` (AA उपप्रमेय)
`therefore" "(AD)/(AB)=(DE)/(BC)`
`rArr" " (AD)/(AD+DB)=(DE)/(BC)" "rArr" " (BC)/(DE)=(AD+BD)/(AD)`
`rArr" " (BC)/(DE)=1+(BD)/(AD)rArr(BC)/(DE)=1+4/5" "(therefore(AD)/(BD)=5/4," दिया है")`
`rArr" " (BC)/(DE)=9/5`
`therefore" "(DE)/(BC)=5/9`
`DeltaDEF" और "DeltaCFB` में
`angle4=angle3" "` (एकान्तर कोण , `thereforeDE"||"BC)`
और `" " angle2=angle1" "` (शीर्षभिमुख कोण)
`therefore" " DeltaDEF~DeltaCBF" "` (AA उपप्रमेय)
`therefore" "(ar(DeltaDEF))/(ar(DeltaCBF))=(DE^2)/(BC^2)=(5/9)^2`
अतः `(ar(DeltaDEF))/(ar(DeltaCBF))=(25)/(81)`