+0

# heeeeelp

0
99
2

The perimeter of a sector of a circle is the sum of the two sides formed by the radii and the length of the included arc. A sector of a particular circle has a perimeter of 28 cm and an area of 49 sq cm. What is the length of the arc of this sector?

Oct 24, 2019

### 2+0 Answers

#1
+11146
+1

The perimeter of a sector of a circle is the sum of the two sides formed by the radii and the length of the included arc. A sector of a particular circle has a perimeter of 28 cm and an area of 49 sq cm. What is the length of the arc of this sector?

Oct 24, 2019
#2
+106539
+1

Area of sector   =   (1/2)r^2 * theta

Perimeter of sector   =  2r + r *theta =   r [ 2 + theta]

Where theta is the measure of the sector's central angle in radians

So

49  =  (1/2)r^2 theta   ⇒  49 / [(1/2) r^2]   =  theta     (1)

28  =  r [ 2 + theta]      (2)

Subbing (1)  into (2)   we have that

28  = r [ 2 +  49 / [(1/2) r^2] ]       simplify

28 =  2r + 98/r

14  = r + 49/r     multiply through by r

14r  = r^2 + 49

r^2  - 14r + 49  = 0

(r - 7)^2  =  0

r  - 7  =  0

r  = 7

So....the arc length of the sector    =

28 - 2(7)  =

28  - 14  =

14 cm

Oct 24, 2019