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CAT 2022 Slot 2 Paper
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© examsnet.com
Question : 66
Total: 66
The length of each side of an equilateral triangle
ABC
is 3 cm. Let
D
be a point on
BC
such that the area of triangle
ADC
is half thearea of triangle
ABD
. Then the length of
AD
, in cm, is
√
8
√
6
√
7
√
Validate
Solution:
Area of triangle
ABD
is twice the area of triangle
ACD
∠
ADB
=
θ
1
2
(
AD
)
(
BD
)
sin
θ
=
2
(
1
2
(
AD
(
CD
)
sin
(
180
−
θ
)
)
)
BD
=
2
CD
Therefore,
BD
=
2
and
CD
=
1
∠
ABC
=
∠
ACB
=
60
°
Applying cosine rule in triangle
ADC
, we get
cos
∠
ACD
=
AC
2
+
CD
2
−
AD
2
2
(
AC
)
(
CD
)
1
2
=
9
+
1
−
AD
2
6
AD
2
=
7
AD
=
√
7
The answer is option C.
© examsnet.com
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