SSC CGL 17 Aug 2021 Shift 1 Paper

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Question : 54 of 100

Marks: +1, -0

In a

△ A B C

, a point

D

lies on

A B

and points

E

and

F

lies on

B C

, such that

D F

is parallel to

A C

and

D E

is parallel to

A F

. If

B E=4 {cm}, E F=6

{cm}

, then find the length (in

{cm}

) of

B C

.

30
20
25
15

Solution:

According to the question,

Given,

D F \| A C

and

D E \| A F

B E=4 {cm}

and

E F=6 {cm}

\;△ B E D-B F A

∴ \;\; \;{B E}/{E F}=\;{B D}/{D A}=\;{4}/{6}=\;{2}/{3}

\;\text " Now, "\;\;∆ B F D ∼ ∆ B C A

∴ \;\; \;{B D}/{D A}=\;{B F}/{F C}=\;{2}/{3}

⇒ \;\; \;{B E+E F}/{F C}=\;{2}/{3}

⇒ \;\; \;{4+6}/{F C}=\;{2}/{3}

\; \;\; F C=\;{30}/{2}=15 {cm}

∴ B C= \;\; B E+E F+F C

= \;\; 4+6+15=25 {cm}

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