The sides of a triangle are k, 1.5k and 2.25k. What is the sum of the squares of its medians ?
- A. 359k^{2}/64
- B. 379k^{2}/64
- C. 389k^{2}/64
- D. 399k^{2}/64 ✓
Correct Answer: D. 399k^{2}/64
Explanation
Sum of squares of medians m_a^2 + m_b^2 + m_c^2 = \frac{3}{4} (a^2 + b^2 + c^2). The sum of squares of the sides is k^2 (1^2 + 1.5^2 + 2.25^2) = k^2(1 + \frac{9}{4} + \frac{81}{16}) = \frac{133}{16}k^2. Therefore, the sum of medians squared is \frac{3}{4} \times \frac{133}{16}k^2 = \frac{399}{64}k^2.
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