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Question
The perimeter of the sector OAB shown in the following figure, is
Options
\[\frac{64}{3} cm\]
26 cm
\[\frac{64}{5} cm\]
19 cm
Solution
We know that perimeter of a sector of radius `r=2r+θ/360xx2pir`
We have given sector angle and radius of the sector and we are asked to find perimeter of the sector OAB.
Therefore, substituting the corresponding values of the sector angle and radius in equation (1) we get,
Perimeter=`2xx7+60/360xx2pixx7c`
We will simplify equation (2) as shown below,
Perimeter=`2xx7+1/6xx2pixx7`
Substituting `pi=22/7` we get
Perimeter=`2xx7+1/6xx2xx22/7xx7`
∴ Perimeter =`2xx7+1/6xx2xx22`
∴ Perimeter =`2xx7+1/3xx22`
∴ Perimeter=`2xx7+22/3`
∴ Perimeter=`14+22/3`
Now we will make the denominator same.
∴ Perimeter=`42/3+22/3`
∴ Perimeter =` (42+22)/3`
∴ Perimeter=`64/3`
Therefore, perimeter of the sector is `64/3 cm`
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