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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.
Solution
(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.
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