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प्रश्न
A wire when bent in the form of an equilateral triangle encloses an area of `121sqrt(3)" cm"^2`. If the same wire is bent into the form of a circle, what will be the area of the circle?
उत्तर
Let a cm be the side of the equilateral triangle.
Now,
Area of the equilateral triangle`=sqrt(3)/4"a"^2`
We have:
`sqrt(3)/4"a"^2 = 121sqrt(3)`
`=> a^2/4 = 121`
⇒ a2 = 484
⇒ a = 22
Perimeter of the triangle = Circumference of the circle
Perimeter of the triangle = (22 + 22 + 22) cm
= 66 cm
Now, let r cm be the radius of the circle.
We know:
Circumference of the circle = 2πr
`=> 2xx22/7xx"r" = 66`
`=> "r"=(66xx7/44)"cm"`
`=> "r" = 21/2 "cm"`
Also,
Area of the circle = πr2
`=(22/7xx21/2xx21/2) "cm"^2`
`=693/2 "cm"^2`
= 346.5 cm2
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