In a triangle ABC, which of the option does not represent the length of the median in terms of its sides.
- $\dfrac{\sqrt{2b^2+2c^2-a^2}}{2}$
- $\dfrac{\sqrt{2b^2+2c^2-2a^2}}{2}$
- $\dfrac{\sqrt{2b^2+2a^2-c^2}}{2}$
- $\dfrac{\sqrt{2c^2+2a^2-b^2}}{2}$
The length of the median m_a to side a is given by the formula m_a = 0.5 * sqrt(2b^2 + 2c^2 - a^2). Option B incorrectly subtracts 2a^2 instead of a^2, making it the incorrect representation.
The length of a median to side a is given by the formula m_a equals one-half times the square root of (2b squared plus 2c squared minus a squared). By rearranging the terms, the formulas for medians to sides b and c are m_b equals one-half times the square root of (2a squared plus 2c squared minus b squared) and m_c equals one-half times the square root of (2a squared plus 2b squared minus c squared). The expression containing 2a squared under the radical is incorrect because it subtracts twice the square of the side instead of the square of the side, so it does not represent a median.