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

Algebra ->  Triangles -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!


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)