# If the area of a rhombus is 48 cm and one of its diagonals is 12 cm find the side of the rhombus

2
by titu3

Log in to add a comment

by titu3

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Some solved examples :

1) The side of a rhombus is 18 cm . Find its perimeter.

Solution :

Perimeter of Rhombus = 4 x side

⇒ = 4 x 18

&rArr = 72 cm

∴ Perimeter of Rhombus = 72 cm.

_________________________________________________________________

2) Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.

Solution :

Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.

AC = 24 ⇒ AO = 12

Let BO = x and AB = 13 cm (given)

By Pythagorean theorem

c 2 = a 2 + b 2

13 2 = 12 2 + x 2 169 = 144 + x 2

x 2 = 169 – 144

x 2 = 25

x = 5 cm

BO = 5 cm

Diagonal BD = 2 x 5 = 10 cm.

Area = ½ x [ product of diagonals]

= ½ x 24 x 10

Area = 120 sq.cm

__________________________________________________________________________

3) If the area of a rhombus is 24 sq.cm and one of its diagonal is 4 cm find the length of the other diagonal.

Solution :

Area = ½ x d1 x d2

24 = ½ x 4 x d2

24 = 2 x d2

d2 = 24/2

d2 = 12 cm

1) The side of a rhombus is 18 cm . Find its perimeter.

Solution :

Perimeter of Rhombus = 4 x side

⇒ = 4 x 18

&rArr = 72 cm

∴ Perimeter of Rhombus = 72 cm.

_________________________________________________________________

2) Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.

Solution :

Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.

AC = 24 ⇒ AO = 12

Let BO = x and AB = 13 cm (given)

By Pythagorean theorem

c 2 = a 2 + b 2

13 2 = 12 2 + x 2 169 = 144 + x 2

x 2 = 169 – 144

x 2 = 25

x = 5 cm

BO = 5 cm

Diagonal BD = 2 x 5 = 10 cm.

Area = ½ x [ product of diagonals]

= ½ x 24 x 10

Area = 120 sq.cm

__________________________________________________________________________

3) If the area of a rhombus is 24 sq.cm and one of its diagonal is 4 cm find the length of the other diagonal.

Solution :

Area = ½ x d1 x d2

24 = ½ x 4 x d2

24 = 2 x d2

d2 = 24/2

d2 = 12 cm

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

where p is the diagonal, and A is the area of the rhombus.