SOLUTION: The length of the median to the hypotenuse of an isosceles, right triangle is 10 units. What is the length of a leg of the triangle, in units? Express your answer in simplest radi

Algebra ->  Triangles -> SOLUTION: The length of the median to the hypotenuse of an isosceles, right triangle is 10 units. What is the length of a leg of the triangle, in units? Express your answer in simplest radi      Log On


   

Question 815424: The length of the median to the hypotenuse of an isosceles, right triangle is 10 units. What is the length of a leg of the triangle, in units? Express your answer in simplest radical form.
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
the median to the hypotenuse forms a new isosceles right triangle with each leg of the original triangle, so each leg length (L) is given by:
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L = sqrt( m^2 + m^2 )
where m is the length of the median
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L = sqrt( 10^2 + 10^2 )
L = sqrt( 2*100 )
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Answer:
L = sqrt(2)*10
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