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Question
The area of a rhombus is 234 cm2. If its one diagonal is 18 cm, find the lengths of its side and the other diagonal. Also, find perimeter of the rhombus.
Solution
Area of a rhombus = 234cm2
Length of one diagonal = d1 = 18cm
Let the side of rhombus be 'a' cm and length of other diagonal be d2 cm.
Now, area of rhombus = `(1)/(2) xx "Product of diagonal"`
⇒ 243 = `(1)/(2) xx "d"_1 xx "d"_2`
234 = `(1)/(2) xx 18 xx "d"_2`
⇒ 234 = 9 x d2
⇒ d2 = `(234)/(9)`
= 26cm
Now,
(Side)2 = `("d"/2)^2 + ("d"_2/2)^2`
= `(18/2)^2 + (26/2)^2`
= 81 + 169
= 250
⇒ Side = `5sqrt(10)"cm"`
Hence, perimeter of a rhombus
= 4 x Side
= `4 xx 5sqrt(10)`
= `20sqrt(10)"cm"`.
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