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Test Index
Geometry Practice Test 1
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© examsnet.com
Question : 8
Total: 40
In ΔABC, D and E are points on AB and AC respectively, such that DE || BC and DE divides the ΔABC into two parts of equal areas. The ratio of AD and BD is:
1 : 1
1 :
√
2
− 1
1 : 2
1 :
√
2
+1
Validate
Solution:
👈: Video Solution
Area of triangle ADE = (Area of DEBC)
⇒ Area of DEBC =
1
2
area of ΔABC
So,
Area
of
Δ
ABC
Area
of
Δ
ADE
=
2
1
The ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding sides.
So,
(
A
B
A
D
)
2
=
2
1
A
B
A
D
=
√
2
1
A
D
+
A
B
A
D
=
√
2
1
1 +
B
D
A
D
=
√
2
1
B
D
A
D
=
√
2
1
−
1
B
D
A
D
=
√
2
−
1
1
A
D
B
D
=
1
√
2
−
1
So, the required ratio = 1 :
√
2
- 1
© examsnet.com
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