Question 1170331
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Let the hypotenuse length be " H "  cm

Then the other leg of the triangle is  {{{sqrt(H^2-4^2)}}} = {{{sqrt(H^2-16)}}} cm.


The area of the triangle is half the product of the legs

       Area = {{{(1/2)*4*sqrt(H^2-16)}}}.


The area can be presented in other way as half the product  of the hypotenuse and the perpendicular L drawn to the hypotenuse

      Area = {{{(1/2)*L*H}}}.


So, we have this equation

     {{{(1/2)*4*sqrt(H^2-16)}}} = {{{(1/2)*L*H}}}.


From this equation, after canceling the factor  {{{(1/2)}}}  in both sides, you get

     L = {{{(4*sqrt(H^2-16))/H}}}.


It is the expression of the length of the altitude via the hypotenuse length.


<U>ANSWER</U>.   L = {{{(4*sqrt(H^2-16))/H}}}.
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Solved.