document.write( "Question 973973: A triangle ABC with ∠ABC = 90 has length of the side AB = 72 and length of BC = 54. What is the length of the perpendicular line from side AC to point B? \n" ); document.write( "
Algebra.Com's Answer #595998 by Boreal(15235)\"\" \"About 
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The hypotenuse, c, is sqrt(8100)=90\r
\n" ); document.write( "\n" ); document.write( "You draw the altitude, and that makes two triangles, each of which is similar to the original. I would draw all three triangles in the same way to show similarity and label them accordingly. \r
\n" ); document.write( "\n" ); document.write( "The whole hypotenuse is to the shorter leg, 54, as the shorter leg, 54, is to the shorter leg of the bisected hypotenuse.\r
\n" ); document.write( "\n" ); document.write( "(90/54)=(54/x)
\n" ); document.write( "2916=90x; x=32.4\r
\n" ); document.write( "\n" ); document.write( "(a/54)=(54/90) also works.
\n" ); document.write( "You don't have to solve for b, although it is easy enough.\r
\n" ); document.write( "\n" ); document.write( "a^2 +h^2=54^2
\n" ); document.write( "(32.4^2)+ h^2 = 2916
\n" ); document.write( "1049.76 +h^2 =2916
\n" ); document.write( "h^2=1866.24
\n" ); document.write( "h=43.2 units ANSWER\r
\n" ); document.write( "\n" ); document.write( "check with b
\n" ); document.write( "(43.2)^2 + 57.6^2=72^2
\n" ); document.write( "1866.24 + 3317.76= 5084\r
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