The area of a rhombus is 96cm² one of its diagonal is 12cm.find their diagonal.
Answers
Answer:
Step-by-step explanation:
Correct option is
B
10 cm
⇒ We have given area of rhombus = 96cm
2
and d
1
=16cm.
⇒ Area of rhombus =
2
1
×d
1
×d
2
⇒ 96=
2
1
×16×d
2
.
∴ d
2
=12cm
⇒ In given figure ABCD is a rhombus.
⇒ Let d
1
=AC=16cm and d
2
=BD=12cm
⇒ We know that diagonals of rhombus perpendicularly bisect each other.
⇒ So, AO=8cm and DO=6cm --- ( 1 )
⇒ In △AOD,
⇒ AD
2
=AO
2
+DO
2
[By using Pythagoras theorem]
⇒ AD
2
=8
2
+6
2
[From (1)]
⇒ AD
2
=64+36
⇒ AD
2
=100
∴ AD=10cm
Hence, we get length of sides of rhombus is 10cm.
Correct option is
B
10 cm
⇒ We have given area of rhombus = 96cm
2
and d
1
=16cm.
⇒ Area of rhombus =
2
1
×d
1
×d
2
⇒ 96=
2
1
×16×d
2
.
∴ d
2
=12cm
⇒ In given figure ABCD is a rhombus.
⇒ Let d
1
=AC=16cm and d
2
=BD=12cm
⇒ We know that diagonals of rhombus perpendicularly bisect each other.
⇒ So, AO=8cm and DO=6cm --- ( 1 )
⇒ In △AOD,
⇒ AD
2
=AO
2
+DO
2
[By using Pythagoras theorem]
⇒ AD
2
=8
2
+6
2
[From (1)]
⇒ AD
2
=64+36
⇒ AD
2
=100
∴ AD=10cm
Hence, we get length of sides of rhombus is 10cm.