OAB is a sector of a circle with centre O and radius 8 cm. Angle AOB = e°
The area of the sector is 58 cm2
Calculate the perimeter of the sector.
Give your answer correct to 3 significant figures.

The perimeter of the sector is :30.5 cm

Step-by-step explanation:

Mathematically, we have the area of the sector as;

e/360 * pi * r^2

r is 8 cm

so we have

58 = e/360 * pi * 8^2

58/64 * 360/pi = e

e = 103.85

To get the perimeter,

we have length of the arc plus 2r

Length of the arc is;

e/360 * 2 * pi * r

add 2 r;

e/360 * 2 * pi * r + 2r

so we have

103.85/360 * 2 * pi * 8 + 2(8)

= 14.5 + 16

= 30.5 cm

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240