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Question

If the perimeter of a sector is 4 times its radius, then the radian measure of the central angle of the sector is (A) 2. (B) 4.(C)2/π.(D)4/π.(E) impossible to determine without knowing the radius.

Solution

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Perimeter = $r+ r+ s$

Perimeter = $2r + r\theta$

Recall that a sector is in the shape of a pie piece, so the perimeter is equal to the straight edge length of the radius $r$, plus the straight edge length of the radius $r$, plus the curved length of the arc $s$. We also know that the arc length is related to the radius $r$ and angle $\theta$ by the following formula: $s = r\theta$.

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