in the figure DE is parallel to BC and AD:DB= 5:4. Find the ratio of ar(triangle DFE) : ar(triangle CFB)
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Answer:
Step-by-step explanation:
∵DE∣∣BC
AD:DB=5:4
ΔADM∼ΔABN
∴
AB
AD
=
AN
AM
9
5
=
AN
AM
_____ (i)
∵
AB
AD
=
BC
DE
9
5
=
BC
DE
______ (ii)
ar(ΔADE)=
2
1
×DE×AM ______ (iii)
ar(ΔABC)=
2
1
×BC×AN _______ (iv)
(iii) & (iv)
ar(ΔABC)
ar(ΔADE)
=
BC
DE
×
AN
AM
=
9
5
×
9
5
ar(ΔABC)
ar(ΔADE)
=
81
25
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