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Standard X
Maths
Question
State true or false:
In
△
A
B
C
,
A
B
=
B
C
=
C
A
=
2
a
and
A
D
is perpendicular to side
B
C
, then
A
D
=
2
a
√
3
True
False
A
False
B
True
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Solution
Verified by Toppr
In
△
s
A
B
D
and
A
C
D
,
∠
A
D
B
=
∠
A
D
C
(Both
90
o
)
A
D
=
A
D
(Common)
A
B
=
A
C
(Given)
Hence,
△
A
B
D
∼
△
A
C
D
(SSA rule)
Hence,
B
D
=
C
D
(By cpct)
Now, in triangle ABD,
A
B
2
=
A
D
2
+
B
D
2
(From Pythagoras theorem)
(
2
a
)
2
=
A
D
2
+
a
2
A
D
2
=
3
a
2
A
D
=
a
√
3
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