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प्रश्न
A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3) "cm"^2`. The same wire is bent to form a circle. Find the area enclosed by the circle.
उत्तर
Area of an equilateral triangle`=sqrt(3)/4xx("Side")^2`
`=> 121sqrt(3) = sqrt(3)/4xx("Side")^2`
`=> 121xx4 = ("Side")^2`
`=> "Side" = 22 "cm" `
Perimeter of an equilateral triangle = 3 × Side
= 3 × 22
= 66 cm
Length of the wire = 66 cm
Now, let the radius of the circle be r cm.
We know:
Circumference of the circle = Length of the wire
2π = 66
`=> 2 xx 22/7xx"r" = 66`
`=> "r" = (66xx7)/(2xx22)`
`=> "r" = 21/2`
⇒ r = 10.5
Thus, we have :
Area of the circle = πr2
`=22/7xx10.5xx10.5`
= 346.5 sq.cm
Area enclosed by the circle = 346.5 cm2
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