Question

The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm; find:
(i) The length of its other diagonal,
(ii) Its area.

Answer 1

Let a be the length of each side of the rhombus.
4a = perimeter
4a = 52
a = 13 cm

(i) It is given that,
AC= 24 cm
We have to find BD.
Now
`a^2 = ( "AC"/2 )^2 + ( "BD"/2)^2`

`13^2 = 12^2 + ("BD"/2)^2`

`( "BD"/2 )^2 = 5^2`

BD = 10 cm
Hence the other diagonal is 10cm.

(ii) Area of the rhombus = `1/2` x AC x BD

                                       = `1/2` x 24 x 10

                                       = 120 sq.cm.