SSC CGL Model Paper 19

Question : 62 of 100

Marks: +1, -0

Points D, E, F divide the sides of triangle ABC in the ratio 1:3, 1:4 and 1:1 as shown in the figure. What fraction of the area of triangle ABC is the area of triangle DEF.

$13/40$
$17/40$
$27/40$
$23/40$

Validate

Solution:

D divides AB into 1:3
E divides BC into 1:4
F divides AC into 1:1

AB = 4c; BD = 3c, DA = c
AC = 2b; AF = b, FC = b
BC = 5a, BE = a, EC = 4a

\text" area of Δ ADF"/\text" area of Δ ABC"

={1/2×c×b\sin \A}/{1/2×4c×2b\sin\A}

=1/8 =5/40

\text" area of Δ FEC"/\text" area of Δ ABC"

={1/2×b×4a\sin\C}/{1/2×2b×5a\sin C}

=4/10=16/40

\text" area of Δ BED"/\text" area of Δ ABC"

={1/2×3c×a\sin\B}/{1/2×5a×4c\sin\B}

=3/20=6/40

\text" area of Δ DEF"/\text" area of Δ ABC"

=1-[{5+16+6}/40]=13/40

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