Question

The area of a rhombus is 216 sq. cm. If it's one diagonal is 24 cm; find:
(i) Length of its other diagonal,
(ii) Length of its side,
(iii) The perimeter of the rhombus.

Answer 1

(i) We know that,
Area of Rhombus = `1/2` x AC x BD
Here
A = 216 sq.cm
AC = 24 cm
BD = ?

Now,
A = `1/2` x AC x BD

216 = `1/2` x 24 x BD

BD = 18 cm.

(ii) Let a be the length of each side of the rhombus.

a² = `("AC"/2 )^2 + ("BD"/2)^2`

a² = 12² + 9²

a² = 225
a = 15 cm

(iii) Perimeter of the rhombus = 4a = 60 cm.