Question

The diagonal of the rhombus is in the ratio of 3:4. If the longer diagonal is 12 cm, then find the area of the rhombus

Answer 1

Answer:

R.E.F image

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

solution

Answer 2

Answer:

the diagonals are 3x and 4x

4x=12

x=3cm

therefore one diagonal 12cm and the other 9cm

area=1/2*product the diagonals

=1/2*12*9

54cm ans