Question

find the length of the arc ,if the perimeter of a sector is 50 cm and radius is 5 cm​

Answer 1

⇒ Perimeter of the sector =50cm

⇒ r is radius of a sector and θ is angle of the sector.

⇒ Perimeter of the sector =

360

o

θ

×2πr+2r

⇒ 50=

360

o

θ

×2πr+2r

⇒ 50−2r=

360

o

θ

×2πr

∴ 2(25−r)=

360

o

θ

×2×πr

∴

πr

(25−r)×360

o

=θ

∴ θ=

π

360

o

(

r

25

−

r

r

)

∴ θ=

π

360

o

(

r

25

−1)

⇒ Area of a sector A=

360

o

θ

×πr

2

Now, substituting value of θ we get,

⇒A=

360

o

π

360

o

(

r

25

−1)

×πr

2

⇒ A=

π×360

o

360

o

(

r

25

−1)×πr

2

⇒ A=r

2

(

r

25

−1)

∴ A=25r−r

2