document.write( "Question 1170331: Do not seem to be able to find the right substitutions to solve the problem.\r
\n" ); document.write( "\n" ); document.write( "Problem: One of the legs of a right triangle has length 4cm. Express the length of the altitude perpendicular to the hypotenuse as a function of the length of the hypotenuse? That is the question.\r
\n" ); document.write( "\n" ); document.write( "So I determined the following relationships from the triangle. I do not know how to draw pictures here so I will try to describe my picture. I have a right triangle with hypothenuse (h). Short side is 4cm, and the other side is side (b).\r
\n" ); document.write( "\n" ); document.write( "After drawing the altitude I have 2 new triangles within the original triangle. The one has side (a) the altitude and side (c) a portion of the original hypotenuse h and the new hypotenuse of the small triangle 4cm.\r
\n" ); document.write( "\n" ); document.write( "The other new triangle has side (h-c) other side (a), and hypotenuse (b)\r
\n" ); document.write( "\n" ); document.write( "So relationships I came up with from pythagorean are:\r
\n" ); document.write( "\n" ); document.write( "1. h^2=16+b^2
\n" ); document.write( "2. 16=a^2+c^2
\n" ); document.write( "3. b^2=(h-c)^2+a^2
\n" ); document.write( "My issue is no matter how I put this together I cannot get to the question \"Express the length of the altitude perpendicular to the hypotenuse as a function of the length of the hypotenuse?\"
\n" ); document.write( "Can you help me?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #795198 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let the hypotenuse length be \" H \"  cm\r\n" );
document.write( "\r\n" );
document.write( "Then the other leg of the triangle is   =  cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area of the triangle is half the product of the legs\r\n" );
document.write( "\r\n" );
document.write( "       Area = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area can be presented in other way as half the product  of the hypotenuse and the perpendicular L drawn to the hypotenuse\r\n" );
document.write( "\r\n" );
document.write( "      Area = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we have this equation\r\n" );
document.write( "\r\n" );
document.write( "      = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this equation, after canceling the factor    in both sides, you get\r\n" );
document.write( "\r\n" );
document.write( "     L = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the expression of the length of the altitude via the hypotenuse length.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.   L = .\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );