Multiple choice

If the perimeter of an equilateral triangle is 12 cm then the length of each median is

  1. $\displaystyle 2\sqrt{5}$ cm
  2. $\displaystyle \sqrt{3}$ cm
  3. $\displaystyle 2\sqrt{3}$ cm
  4. $\displaystyle 3\sqrt{2}$ cm
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C Correct answer
Explanation

Perimeter = 12, so side = 4. In an equilateral triangle, the median is also the altitude. Altitude = (sqrt(3)/2) * side = (sqrt(3)/2) * 4 = 2 * sqrt(3).

AI explanation

An equilateral triangle with a perimeter of 12 cm has each side measuring 4 cm. The length of a median in an equilateral triangle is given by the formula (side * sqrt(3)) / 2. Substituting the side length gives (4 * sqrt(3)) / 2, which equals 2 * sqrt(3) cm.

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