Multiple choice

If the perimeter of a circle is $P$ cm then find the length of an arc of the circle which subtends $\displaystyle 144^{\circ}$ at the centre of the circle (in cm).

  1. $\dfrac {2P}{5}$
  2. $\dfrac {3P}{5}$
  3. $\dfrac P5$
  4. $\dfrac {4P}{5}$
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A Correct answer
Explanation

Arc length = (theta / 360) * 2 * pi * r. Perimeter P = 2 * pi * r. Arc length = (144 / 360) * P = (2/5) * P.

AI explanation

The length of an arc is found by multiplying the circumference by the fraction of the central angle over 360 degrees. Substituting the given perimeter as the circumference and the angle as 144 degrees, the arc length equals P times 144/360. Since 144/360 simplifies to 2/5, the arc length is 2P divided by 5.