document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158306>Question 1158306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the altitude drawn to the hypotenuse of a right triangle EFG partitions it into two segments of lengths of 8 and 10, then find the length of the longer leg of triangle EFG in simplest radical form. </SPAN>\n" );
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document.write( "By similar triangles, the length of the altitude to the hypotenuse of a right triangle is equal to the geometric mean of the lengths of the two segments of the hypotenuse:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+sqrt%288%2A10%29 ALIGN=MIDDLE  ALT=\"h+=+sqrt%288%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+=+8%2A10+=+80 ALIGN=MIDDLE  ALT=\"h%5E2+=+8%2A10+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the length of the longer leg of triangle EFG is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2810%5E2%29%2Bh%5E2%29+=+sqrt%28100%2B80%29+=+sqrt%28180%29+=+6%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2810%5E2%29%2Bh%5E2%29+=+sqrt%28100%2B80%29+=+sqrt%28180%29+=+6%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );