length of diagonals if a rhombus is 9 cm and its height is 24cm find its area
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Answer:
We know that the diagonals of a rhombus bisect each other at right angles.
∴
A
O
=
O
C
=
24
2
=
12
c
m
B
O
=
O
D
=
18
2
=
9
c
m
Consider right-angled triangle
Δ
A
O
B
,
From pythagoras theorem, we have
A
B
2
=
A
O
2
+
B
O
2
=
(
12
)
2
+
(
9
)
2
=
144
+
81
⇒
A
B
2
=
225
⇒
A
B
=
√
(
15
)
2
∴
A
B
=
15
c
m
Hence, the measure of each side of given rhombus is
=
15
c
m
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