Hunting for the Hypotenuse
Geometry
Level
4
In a right angled triangle ABC right angled at C , medians AQ and BP intersect at point O. If the lengths of medians are 2 and 3 units respectively , find the value of
The answer is 10.4.
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By Pythagoras: CQ^2 + AC^2 = 4,and BC^2 + PC^2 = 9. By addition, we get CQ^2 + PC^2 +AC^2 + BC^2 = 13. 1/4 (BC^2 + AC^2) + AC^2 + BC^2 = 13. So 5/4 AB^2= 13, or AB^2=10.4