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Question
The area of rhombus is `480cm^2` , and one of its diagonal measures 48 cm. Find
(i) the length of the other diagonal,
(ii) the length of each of the sides
(iii) its perimeter
Solution
(i) Area of a rhombus, =` 1/2xxd_1xxd_2`, Where `d_1 and d_2` are the lengths of the diagonals.
⇒ `480=1/2xx48xxd_2`
⇒`d_2=(480xx2)/48`
⇒ `d_2=20 cm`
∴ Length of the other diagonal=`20cm`
(2) side=`1/2 sqrt(d_1^2-d_2^2)`
= `1/2sqrt(48^2+20^2)`
=`1/2sqrt(2304+400)`
=`1/2sqrt2704`
=`1/2xx52`
=`26 cm`
∴ Length of the side of the rhombus =`26cm`
(iii) Perimeter of the rhombus=`4xx"side"`
=`4xx26`
=`104 cm`
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