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

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#### 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`

Concept: Circumference of a Circle

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