Problem: In triangle , the median from vertex is perpendicular to the median - from vertex . If the lengths of sides and are and respectively, then the length of side is
Answer Choices:
A.
B.
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E.
Solution:
Let the medians be and which intersect at O and let AO and BO have lengths and so that and have lengths and respectively. From right triangles AON and BOM, we obtain
Four-fifths of the sum of these two equations gives which is the square of the hypotenuse of right triangle . Hence .
