Anonymous

# Perimeter & Area of a sector of a circle?

I do not know how to find the radii of a sector in a circle if the sector has a perimeter of 7cm and an area of 3sq.cm

Relevance

set up simultaneous equations

0.5 X R X R X sector angle = 3

2R + (R X Sector Angle) = 7

solve for R

• Let r = radius of the circle

f = fraction of the circle that make up the sector.

Perimeter = 2 pi r f + 2r = 7

Area = pi r^2 f = 3 pi f = 3/r ^ 2

by substitution

6/r + 2r = 7

2 r^2 - 7r + 6 = 0

(2r -3)(r-4)=0

r = 3/2 or 4

• you are able to desire to artwork out the fraction of the section/perimeter that's contained interior the international. it is, handily, the ratio of the attitude on the centre of the international to the entire attitude (360 stages). i.e. if P=perimeter of circle p=arc of sector, A and a are comparable for section, then: p/P=a/A=40/360=a million/9. So now all you are able to desire to do is calculate A=pi*r^2, and P=2*pi*r, and remedy the equations p/P=a million/9 & a/A=a million/9 to discover p and a. ascertain you upload two times the radius to p to get the entire perimeter of the international. solid success :)

• Perimeter: 2r + x2πr = 7

2r + x2πr - 7 = 0

Area: xπr² = 3

xπr² - 3 = 0

2r + x2πr - 7 = xπr² - 3

xπr² - 2r(1 + xπ) + 4 = 0

Oh, boy...I'm lost.