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