the length of a rhombus is equal to to the length of a square and the length of diagonal of square is 40root2 cm. if the length of the diagonals of the rhombus are in ratio 3:4,then let us write by calculating the area of the field in shape of rhombus
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Let the sides of rhombus be a
and diagonals be d
1
and d
2
perimeter =40cm
4a=40cm
a=10cm
Ratio of diagonals=3:4
d
2
d
1
=
4
3
d
1
=
4
3d
2
...(1)
Now,
a
2
=
4
d
1
2
+
4
d
2
2
d
1
2
+d
2
2
=4a
2
16
9d
2
2
+d
2
2
=4(10)
2
16
25d
2
2
=400
Square Rooting both sides
4
5d
2
=20
d
2
=16
put d
2
=16 in equation ...(1)
d
1
=12
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