Q39.The perimeter of a rhombus is 20 cm. If one of its diagonals is 6 cm, then its area is (a) 24 cm square (b) 20 cm square (C) 36 cm square (d) 28 cm square
Answers
Answer:
Solution
verified
Verified by Toppr
Let first diagonal be d
Second diagonal be d
2
Giver perimeter of a rhombus =20cm
We know perimeter of a rhombus =4 sides
Hence, side =
4
20
cm=5cm
Now, we know that the diagonals of a rhombus bisect each other at right angles (90°)
Hence, a right angled triangle can be visualized with side as hypotenuse.
Diagonal length =8cm
Half the length ( since diagonal bisect each other ) =
2
8
=4cm
⇒(
2
d
)
2
+(
2
d
2
)
2
=5
2
⇒(
2
8
)
2
+(
2
d
2
)
2
=25
⇒4
2
+(
2
d
2
)
2
=25
⇒(
2
d
2
)
2
=25−16
⇒(
2
d
2
)
2
=9
⇒(
2
d
2
)
2
=
9
⇒
2
d
2
=3
⇒d
2
=6cm
Hence other diagonal =6cm
Area =
2
1
×d×d
2
=
2
1
×8×6
=24cm
2
.
Hence, the answer is 24cm
2
.
Answer:
This is your answer in the Given pic
Hope it helps
Please Mark Me Brainliest
