Multiple choice

In $\triangle XYZ, \angle Y = 90^{\circ}$, if the lengths of the medians drawn from $X$ and $Z$ are $5$ and $\sqrt {40}$, find the length of the hypotenuse

  1. $10$
  2. $\sqrt {13}$
  3. $2\sqrt {40}$
  4. $2\sqrt {13}$
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D Correct answer
Explanation

In a right triangle, medians m_x and m_z satisfy 4(m_x^2 + m_z^2) = 5 * hypotenuse^2. 4(25 + 40) = 5 * h^2. 4(65) = 5 * h^2. 260 = 5 * h^2. h^2 = 52. h = sqrt(52) = 2*sqrt(13).

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