Question

Find the diagonal AC if the side of rhombus field 12m and diagonal BD is 20m?
A) 2√11m B) 4√11m C) 6√11m D) 8√11m8​

Answer 1

Answer:

(i) It is given that

Area of rhombus = 480 cm

2

It can be written as

2

1

×d

1

×d

2

=480

So we get

2

1

×48×d

2

=480

On further calculation

d

2

= 20cm

(ii) Consider AC = 48cm and BD = 20cm

The diagonals of a rhombus bisect at right angles

Consider Δ AOD,

Using the Pythagoras theorem

AD

2

=OD

2

+AO

2

By substituting the values

AD

2

=24

2

+10

2

On further calculation

AD

2

=576+100

By addition

AD

2

=676

By taking out the square root

AD=

676

So we get

AD = 26 cm

We know that AD = BC = CD = AD = 26 m

Therefore, the length of each side of rhombus is 26cm.

(iii) We know that

Perimeter of a rhombus = 4 (side)

By substituting the value of side from above

Perimeter of a rhombus = 4 (26)

So we get

Perimeter of a rhombus = 104 cm

solution