The diagonals of a rhombus are in the ratio 3:4. If its perimeter is 80 cm, find the lengths of the sides and diagonals of the rhombus
Answers
Answered by
6
Step-by-step explanation:
Let ABCD is a rhombus in which diagonal AC=3k unit ,BD=4k unit ,which meet at O. let AB=BC=CD=DA=perimeter/4= 40/4=10 unit.
In right angled triangle AOB
OA^2+OB^2=AB^2
(AC/2)^2+(BD/2)^2=(10)^2
9/4.k^2+ 4.k^2=100
25/4.k^2=100
k^2=16
k=4
Diagonal AC=3k = 3×4 =12 unit.
Diagonal BD=4k=4×4=16 unit.
each side= 10 unit , Answer
Answered by
7
Answer:
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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