pls solve this question
it's urgent ... solve correctly I'll marks as brainliest
Answers
Answer:
25/81.SEE THE ATTACHMENT FOR EXPLANATION!!
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
Step-by-step explanation:
In Triangle DFE and triangle CFB;
Because DE II BC therefore,
<1 = <4 ( alt. int. angles )
<2 = <3 ( alt. int. angles )
<DFE = <BFC ( vertically opposite angles )
Therefore, triangle DFE is congruent to triangle CFB.
=> area of triangle DFE = area of triangle CFB
____ eq.1
Letting area of triangle DFE be x. Therfore,
eq.1 is x = x
=> area of triangle DFE / area of triangle CFB
=> x / x
=> 1