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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.
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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