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Standard VIII
Mathematics
Rhombus
Question
In the rhombus ABCD, AC and BD are the diagonals. If the diagonals are
16 cm and 12 cm
. Find the length of each of its sides.
12 cm
9 cm
8 cm
10 cm
A
10 cm
B
12 cm
C
9 cm
D
8 cm
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Solution
Verified by Toppr
We know that, diagonals in a rhombus bisect each other perpendicularly.
Let
O
is the intersecting point of diagonals
A
C
and
B
D
.
O
A
=
A
C
2
=
16
2
=
8
c
m
O
B
=
B
D
2
=
12
2
=
6
c
m
Now, in
△
A
O
B
,
∠
A
O
B
=
90
o
⇒
(
A
B
)
2
=
(
O
A
)
2
+
(
O
B
)
2
[ By Pythagoras theorem ]
⇒
(
A
B
)
2
=
(
8
)
2
+
(
6
)
2
⇒
(
A
B
)
2
=
64
+
36
⇒
(
A
B
)
2
=
100
∴
A
B
=
10
c
m
We know that, all sides of rhombus are equal.
∴
The length of each side of rhombus is
10
c
m
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