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# The perimeter of a sector is 16 cm, the area is 15 cm^2. Find r and s?

Can you guys help with this?

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- MichaelLv 78 years agoFavorite Answer
I suppose "sector" is the part of a circle

like the part of a pizza, ok?

well, then we have

p = 16 cm

a = 15 cm²

s/r is the angle of the sector

and

equation1 : p = 2r + s

and

a in so that (ratio of angles) = (ratio of surfaces)

equation2 : (s/r)/2Pi = a/ (Pi * r²)

so

s = 2a / r

if we replace this result

in equation (1) we get:

p = 2r + 2a/r

so

pr = 2r² + 2a

and r is solution of equation

2r² - pr + 2a = 0

with the values of a and p, we get

2r² - 16r + 2 * 15 = 0

r² -8r + 15 = 0

delta = (-8)² - 4*(1)*(15) = 64 - 60 = 2²

so possible solutions for r are

r = (8 +/- 2) / 2

so

r1 = 3 and

r2 = 5

for r1 = 3 we get s1 = 2a/r1 = 30/3 = 10 and

for r2 = 5 we get s2 = 2a/r2 = 30/5 = 6

hope it'll help !!!

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