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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  • 8 years ago
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    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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