n the rhombus ABCD, AC and BD are the diagonals. If AC= 12cm and BD= 16cm, find the length of the side of the rhombus.
Answers
Answered by
9
Answer:
10 cm
Step-by-step explanation:
Attachments:
Answered by
0
Answer:
10 cm
Step-by-step explanation:
We know that, diagonals in a rhombus bisect each other perpendicularly.
Let O is the intersecting point of diagonals AC and BD.
OA=
2
AC
=
2
16
=8cm
OB=
2
BD
=
2
12
=6cm
Now, in △AOB,∠AOB=90
o
⇒ (AB)
2
=(OA)
2
+(OB)
2
[ By Pythagoras theorem ]
⇒ (AB)
2
=(8)
2
+(6)
2
⇒ (AB)
2
=64+36
⇒ (AB)
2
=100
∴ AB=10cm
We know that, all sides of rhombus are equal.
∴ The length of each side of rhombus is 10cm
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