Relation between Areas and Sides of Similar Triangles
area of Δ DOE...
Question
In the given figure, DE || BC and AD : DB = 5 : 4, then areaofΔDOEareaofΔDCE is
A
15 : 4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
25 : 16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
5 : 14
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
25 : 196
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C 5 : 14 Given, ADDB=54 ⇒ADAD+DB=55+4⇒ADAB=59 In ΔADE and ΔABC, ∠ADE=∠ABC [corresponding angles] and ∠A=∠A [common] ∴ΔADE∼ΔABC, [by AA similarity] ⇒DEBC=ADAB=59⇒DE:BC=5:9 Now, in ΔDOE and ΔCOB, ∠OED=∠OBC [alternate angles] ∠DOE=∠BOC [vertically opposite angles] ∴ΔDOE∼ΔCOB [by AA similarity] ⇒DOOC=DEBC=59⇒DOOD+OC=55+9⇒DODC=514 Now, draw EN⊥CD ∴AreaofΔDOEAreaofΔDCE=12×DO×EN12×DC×EN=DODC=514