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प्रश्न
The area of a sector whose perimeter is four times its radius r units, is
विकल्प
\[\frac{r^2}{4}\]
2r2 sq. units
r2 sq.units
उत्तर
We know that perimeter of the sector= `2r+θ/360xx2pir`
We have given that perimeter of the sector is four times the radius.
`2r+θ/360x2pir=4r`
Subtracting 2r from both sides of the equation,
`∴ θ/360xx2pir^=4r-2r`
`∴ θ/360xx2pir=2r`
Dividing both sides of the equation 2r we get,
`θ/360=pi=1`
`∴ θpi/360=1`.............(1)
Let us find the area of the sector.
∴ Area of the sector=`θ/360 pir^2`
Substituting `θpi/360=1` we get,
Area of the sector=`r^2`
Hence, area of the sector is `r^2 `sq.units
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