Question

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​

Answer 1

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

Answer 2

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