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1. Help? Not sure what to do on this question?
2. (Original post by Bhansongal98)
Help? Not sure what to do on this question?
Find an expression for the area of the sector, and another for the perimeter involving and .
Solve the latter for using the given condition on the perimeter and arc length then substitute this to find in the first.
3. (Original post by joostan)
Find an expression for the area of the sector, and another for the perimeter involving and .
Solve the latter for using the given condition on the perimeter and arc length then substitute this to find in the first.
What expression should I use for the perimeter?
4. (Original post by Bhansongal98)
What expression should I use for the perimeter?
Well you are given that , you can also calculate the perimeter in the conventional way by summing the lengths of the sides.
5. (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?
6. (Original post by Bhansongal98)
Help? Not sure what to do on this question?
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.
7. (Original post by HapaxOromenon)
Note: I write t instead of theta.
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