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UPSC CDS Math Triangles Questions
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© examsnet.com
Question : 48
Total: 68
Suppose ABC is a triangle with AB of unit length. D and E are the points lying on AB and AC respectively such that BC and DE are parallel. If the area of triangle ABC is twice the area of triangle ABE, then the length of AD is
[2016 CDS-I]
1
2
unit
1
3
unit
1
√
2
unit
1
√
3
unit
Validate
Solution:
Here DE || BC
In ΔADE and ΔABC
∠ADE = ∠ABC(Corresponding angles)
∠AED = ∠ACB (Corresponding angles)
∴ ΔADE ~ ΔABC(AA Similarity)
⇒
a
r
(
Δ
A
D
E
)
a
r
(
Δ
A
B
C
)
=
(
A
D
A
B
)
2
⇒
(
A
D
1
)
2
=
a
r
(
Δ
A
D
E
)
2
×
a
r
(
Δ
A
D
E
)
=
1
2
⇒
A
D
=
1
√
2
© examsnet.com
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