## About "Perimeter of a sector"

Perimeter of sector :

Here we are going to see formula to find perimeter of any sector with example problems.

Formula :

Perimeter of the sector = L + 2r

L - length of sector

Now let us see some example problems based on this formula.

Example 1 :

Find the perimeter of the sector whose area is 324 square cm and the radius is 27 cm.

Solution :

To find perimeter of any sector we need length of arc and radius of sector. In this question we have radius but we don't have length of arc to find L we are using the formula (1/2) L r instead of area of sector.

Area of sector = 324 square units

(1/2) L x r = 324

here r = 27 cm

(1/2) x L x 27 = 324

L = (324 x 2)/27

L = 12 x 2

L = 24 cm

Now we can find the perimeter.

Perimeter of a sector = L + 2r

=  24 + 2(27)

=  24 + 54

=  78 cm  perimeter of the sector

Example 2 :

Find the length of arc if the perimeter of the sector is 45 cm and radius is 10 cm.

Solution :

Perimeter of sector = 45 cm

Perimeter of sector = L + 2r

L + 2r = 45

here r = 10 cm

L + 2 (10) = 45

L + 20 = 45

L = 45 - 10

L = 35 cm

Example 3 :

Find the radius of sector whose perimeter and length of arc are 30 cm and 16 cm respectively.

Solution :

Perimeter of sector = 30 cm

length of arc = 16 cm

Perimeter of sector = L + 2r

L + 2r = 30

16 + 2r = 30

2r = 30 - 16

2r = 14

r = 14/2

r = 7 cm.

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