The perimeter of a rhombus is 60 cm. If one of its diagonal us 18 cm long, find

(i) the length of the other diagonal, and

(ii) the area of the rhombus.

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#### Solution

Perimeter of a rhombus = 4a (Here, a is the side of the rhombus)

⇒ `60=4a `

⇒ `a=15`

(i) Given:

One of the diagonals is 18 cm long

`d_1= 18cm`

Thus, we have:

Side= `1/2sqrt(d_1^2+d_2^2)`

⇒ `15=1/2sqrt(18^2+d_2^2)`

⇒`30=sqrt(18^2+d_2^2)`

Squaring both sides, we get:

⇒`900=18^2+d_2^2`

⇒`900=324+d_2^2`

⇒`d_2^2=576`

⇒`d_2^2=24cm`

(ii) Area of the rhombus=`1/2d_1xxd_2`

=`1/2xx18xx24`

=`216 cm^2`

Concept: Circumference of a Circle

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