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    (Original post by Bhansongal98)
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    Find an expression for the area of the sector, and another for the perimeter involving r and \theta.
    Solve the latter for \theta using the given condition on the perimeter and arc length then substitute this to find r in the first.
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    (Original post by joostan)
    Find an expression for the area of the sector, and another for the perimeter involving r and \theta.
    Solve the latter for \theta using the given condition on the perimeter and arc length then substitute this to find r in the first.
    What expression should I use for the perimeter?
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    (Original post by Bhansongal98)
    What expression should I use for the perimeter?
    Well you are given that P=4AB, you can also calculate the perimeter in the conventional way by summing the lengths of the sides.
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    (Original post by Bhansongal98)
    What expression should I use for the perimeter?
    so you know the formula to find the arc length in radians right?
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    (Original post by Bhansongal98)
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    Note: I write t instead of theta.

    Area sector = 12, so r^2*t/2 = 12 -> r^2 * t = 24.
    Arc length AB = r*t.
    -> Perimeter = Arc length + 2 Radii = r * t + 2* r.
    We hence have that r * t + 2 * r = 4 * r * t - > 2 * r = 3 *r * t -> dividing by r (as r can't be 0), 2 = 3t -> t = 2/3.
    Hence r^2 * 2/3 = 24 -> r^2 = 24 / (2/3) = 36 -> Since r is positive, r = 6.
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    (Original post by HapaxOromenon)
    Note: I write t instead of theta.
    Full solutions are against forum guidelines, kindly delete or edit your answer.
 
 
 
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