Question

10) Diagonals AC and BD of a rhombus ABCD intersect at O. If AC = 16 cm, BD = 12 cm, find the length of its sides.

Answer 1

Answer:

ANSWER

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

solution