document.write( "Question 288311: the altitude of a right triangle splits the hypotenuse into two segments of length 4 and 16. what is the length of the altitude? \n" ); document.write( "
Algebra.Com's Answer #208979 by dabanfield(803)\"\" \"About 
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Let x and y be the two legs of the rigth triables and a be the altitute. The altitute a creates two more right triable, one with sides a, 4 and hypotenuse y and theother with sdes a, 16 and hypotenuse x.\r
\n" ); document.write( "\n" ); document.write( "From the Pythagorean Theorem we have then:\r
\n" ); document.write( "\n" ); document.write( "x^2 + y ^2 = (16 + 4)^2 or
\n" ); document.write( "1.) x^2 + y^2 = 400\r
\n" ); document.write( "\n" ); document.write( "We also have:\r
\n" ); document.write( "\n" ); document.write( "2.) y^2 = a^2 + 4^2 and
\n" ); document.write( "3.) x^2 = a^2 + 16^2\r
\n" ); document.write( "\n" ); document.write( "Adding the two equations above we have:\r
\n" ); document.write( "\n" ); document.write( "x^2 + y^2 = 2*a^2 + 4^2 + 16^2 or\r
\n" ); document.write( "\n" ); document.write( "4.) x^2 + y^2 = 2*a^2 + 272\r
\n" ); document.write( "\n" ); document.write( "From 1.) we have x^2 + y^2 = 400 so 4.) becomes:\r
\n" ); document.write( "\n" ); document.write( "400 = 2*a^2 + 272
\n" ); document.write( "2*a^2 = 400 - 272
\n" ); document.write( "2*a^2 = 128
\n" ); document.write( "a^2 = 64
\n" ); document.write( "a = sqrt(64)
\n" ); document.write( "a = 8\r
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