Multiple choice

In a triangle, the side lengths are $a = 5, b = 3$ and $c = 4$. Find the length of the median drawn to the side $a$.

  1. $1.5$
  2. $2.5$
  3. $3.5$
  4. $4.5$
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B Correct answer
Explanation

The sides are 3, 4, and 5, which form a right-angled triangle because 3^2 + 4^2 = 5^2. The median to the hypotenuse (side a=5) in a right triangle is half the length of the hypotenuse, which is 5/2 = 2.5.

AI explanation

Applying the Apollonius's theorem, the length of the median drawn to side a is calculated as m = 0.5 * sqrt(2*b^2 + 2*c^2 - a^2). Substituting the given values a = 5, b = 3, and c = 4, we get m = 0.5 * sqrt(2*(3^2) + 2*(4^2) - 5^2). This simplifies to m = 0.5 * sqrt(18 + 32 - 25), resulting in m = 0.5 * sqrt(25) = 2.5.

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