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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.
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Solution
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.
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