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Byju's Answer
Standard X
Mathematics
Perpendicular from Right Angle to Hypotenuse Divides the Triangle into Two Similar Triangles
In a triangle...
Question
In a triangle JKL, the internal bisector of the angle J meets JL = 3 and
∠
J
=
60
∘
.
The length JM is
A
2
√
3
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B
12
√
3
7
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C
15
√
3
8
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D
None of these
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Solution
The correct option is
B
12
√
3
7
Let KL = x and JM = y, Using bisector theorem,
K
M
M
L
=
J
K
J
L
=
4
3
T
h
u
s
,
K
M
=
4
x
7
a
n
d
M
L
=
3
x
7
Now, in triangle JKM, using cosine rule,
C
o
s
30
∘
=
{
4
2
+
y
2
−
16
x
2
49
}
2
×
2
y
⇒
4
√
3
y
=
{
16
+
y
2
−
16
x
2
49
}
.
.
.
.
(
1
)
Similarly in triangle JML,
C
o
s
30
∘
=
{
3
2
+
y
2
−
9
x
2
49
}
2
×
3
y
⇒
3
√
3
y
=
{
9
+
y
2
−
9
x
2
49
}
e
q
(
2
)
From eqs (1) and (2), we get
y
=
12
√
3
7
Thus, Option (b) is correct.
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