document.write( "Question 674558: The diagonal, d of a box can be found using the formula d = where l, w, and h , represent the length, width and height of the box. If the box is 24 cm in length, 8 cm in width, and 6 cm in height, then what is the length of the diagonal? \n" ); document.write( "
Algebra.Com's Answer #419324 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You inadvertently left out the formula, so I'll do it without the formula\r\n" );
document.write( "first and then again with a formula.  \r\n" );
document.write( "\r\n" );
document.write( "We want the length of the red line DB, which is the\r\n" );
document.write( "diagonal of the box.  \r\n" );
document.write( "\r\n" );
document.write( "There are two right triangles ABC and DBC.\r\n" );
document.write( "\r\n" );
document.write( "First we calculate the hypotenuse BC of right triangle\r\n" );
document.write( "ABC using the Pythagorean theorem:\r\n" );
document.write( "\r\n" );
document.write( " BC² = AC² + AB²\r\n" );
document.write( " BC² = 8² + 24²\r\n" );
document.write( " BC² = 64 + 576\r\n" );
document.write( " BC² = 640\r\n" );
document.write( " BC = √640\r\n" );
document.write( " BC = 8√10\r\n" );
document.write( "\r\n" );
document.write( "The required diagonal, the red line DB is the hypotenuse of\r\n" );
document.write( "right triangle DBC.  So we use the Pythagorean theorem again\r\n" );
document.write( "\r\n" );
document.write( "DB² = DC² + BC²\r\n" );
document.write( "DB² = 6² + 640   (Notice we only needed BC², not BC)\r\n" );
document.write( "DB² = 36 + 640\r\n" );
document.write( "DB² = 676\r\n" );
document.write( " DB = √676\r\n" );
document.write( " DB = 26\r\n" );
document.write( "\r\n" );
document.write( "So the diagonal DB is 26 cm in length, without using the formula,\r\n" );
document.write( "but only the Pythagorean theorem.\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "The formula you omitted is:\r\n" );
document.write( "\r\n" );
document.write( "d = √L² + W² + H² \r\n" );
document.write( "\r\n" );
document.write( "Substituting gives\r\n" );
document.write( "\r\n" );
document.write( "d = √L² + W² + H²\r\n" );
document.write( "\r\n" );
document.write( "d = √24² + 8² + 6²\r\n" );
document.write( "\r\n" );
document.write( "d = √576 + 64 + 36\r\n" );
document.write( "\r\n" );
document.write( "d = √676\r\n" );
document.write( "\r\n" );
document.write( "d = 26 cm\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );