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3 years ago

Perimeter = 210cm Calculate the radius of the sector Angle is 30

Mathematics

1 answer:

marin [14]3 years ago

7 0

Answer:

Step-by-step explanation:

Let the length of the arc of the sector which subtend angle of 30°,2πrx°/360 where x°=30°, this can also be written as πrx°/180 .Perimeter of a sector

2r+ arc length.

Now let the arc length = 22/7 x r x 30/180; this gives, 11r/21cm. Therefore the perimeter = r + r + 11r/21 = 210.

Solving for r in the equation

2r + 11r/21 = 210, multiply through by 21, we now have 42r + 11r = 4410

53r = 4410; divide through by 53, r = 83.2cm. Therefore the length of the arc = 11r/21, 11 x 83.2/21 = 43.6cm.

Check: 2r + 11r/21, 2 x 83.2 + 43.6 = 210cm.

Therefore the radius of the sector

r = 83.2cm.

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