SOLUTION: In right triangle ABC, the median to the hypotenuse has length 15 units and the altitude to the hypotenuse has length 12 units. What is the length of the shorter leg of triangle AB
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Question 393671: In right triangle ABC, the median to the hypotenuse has length 15 units and the altitude to the hypotenuse has length 12 units. What is the length of the shorter leg of triangle ABC? Express your answer in simplest radical form. Answer by ewatrrr(24785) (Show Source):
Hi
Note: median of 15 units bisects the hypotenuse into two equal lengths of 15
that is: the distance along the hyp from the alt to the short side = 6
15 - sqrt(15^ - 12^) = 6
the length of the shorter leg is 6sqrt(5) in simplest radical form
12^2 + 6^2 = sqrt(180) = 6sqrt(5)