The perimeter of a sector is 16 cm, the area is 15 cm^2. Find r and s?
Can you guys help with this?
- 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
equation1 : p = 2r + s
a in so that (ratio of angles) = (ratio of surfaces)
equation2 : (s/r)/2Pi = a/ (Pi * r²)
s = 2a / r
if we replace this result
in equation (1) we get:
p = 2r + 2a/r
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
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 !!!