Question

the perimeter of the rombus is 160 cm and it's one diagonal 10 cm long . the length of other diagonal is
​

Answer 1

Step-by-step explanation:

"Given that Perimeter of rhombus ABCD=160cm ⇒4× side =160⇒ side =40cm

Since all sides of a rhombus are equal, so, AB=BC=CD=DA=40cm

Now, diagonal AC=10cm

As we know that the diagonals of a rhombus bisect each other at 90

0

, so AO=OC=5cm

In △AOB, AO=5cm and AB=40cm.

By Pythagoras theorem, AB

2

=AO

2

+OB

2

So,40

2

=5

2

+OB

2

On solving we get, OB

2

=1575⇒OB=15

7

⇒BD=2×OB⇒BD=30

7

So, the second diagonal is of length 30

7

cm

Answer 2

Answer:

"Given that Perimeter of rhombus ABCD=160cm ⇒4× side =160⇒ side =40cm

Since all sides of a rhombus are equal, so, AB=BC=CD=DA=40cm

Now, diagonal AC=10cm

As we know that the diagonals of a rhombus bisect each other at 90

0

, so AO=OC=5cm

In △AOB, AO=5cm and AB=40cm.

By Pythagoras theorem, AB

2

=AO

2

+OB

2

So,40

2

=5

2

+OB

2

On solving we get, OB

2

=1575⇒OB=15

7

⇒BD=2×OB⇒BD=30

7

So, the second diagonal is of length 30

7

cm