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jmc

geometry intermediate

Problem

A right triangle has leg lengths of 8 and 15 units. What is the length, in units, of the median to the hypotenuse? Express your answer as a common fraction.
Solution
, so the hypotenuse has length . The median to the hypotenuse of a right triangle is a radius of the circumcircle, while the hypotenuse is a diameter. So the median is half as long as the hypotenuse, and thus has length .
Final answer
\frac{17}{2}