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Question

In figure, DEBC and AD:DB=5:4 . Find Area(ADE)Area(ABC).
1506366_0f6d208f1f5042e9bd50b23dd0e7b8ad.jpg

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Solution


DE||BC

AD:DB=5:4

ΔADMΔABN

ADAB=AMAN

59=AMAN _____ (i)

ADAB=DEBC

59=DEBC ______ (ii)

ar(ΔADE)=12×DE×AM ______ (iii)

ar(ΔABC)=12×BC×AN _______ (iv)

(iii) & (iv)

ar(ΔADE)ar(ΔABC)=DEBC×AMAN

=59×59

ar(ΔADE)ar(ΔABC)=2581

1207009_1506366_ans_5bd0db6428c8433fb23fa03886a45cdc.PNG

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