Question

The digonals of roumbus12cm and 16cm . The length of the side of roumbus is​

Answer 1

Let ABCD be the rhombus and AC and BD bisect at point O. AC = 16cm and BD = 12cm.

⇒ We know that the diagonals of rhombus bisect at right angles.

⇒ AO=

2

16

=8cm

⇒ BO=

2

12

=6cm

⇒ In right angled △AOB,

By using Pythagoras theorem,

⇒ AB

2

=AO

2

+BO

2

⇒ AB

2

=8

2

+6

2

⇒ AB

2

=64+36

⇒ AB

2

=100

⇒ AB=100

⇒ AB=10cm

∴ Side of a rhombus is 10cm.

Answer 2

Answer:

Answer⤵

Let ABCD be rhombus with AC and BD diagonals.

Let AC and BD bisect at O.

Therefore AO = 16/2=8 BO = 12/2=6cm

In right angled triangle AOB, by Pythagoras theorem we can write as AB2=AO2+OB2

AB2=82+62

AB2= 64 + 36

AB= √ 100

AB =10

Length of rhombus is 10 cm