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प्रश्न
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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उत्तर
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`
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