document.write( "Question 1182434: The length of rectangular solids is four times the width and the height is twice the width.
\n" ); document.write( "Find the volume and the length of its diagonal if the total surface area is 198 in2 \n" ); document.write( "

Algebra.Com's Answer #812444 by ikleyn(52903) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The length of rectangular solids is four times the width and the height is twice the width.
\n" ); document.write( "Find the volume and the length of its diagonal if the total surface area is 198 in2
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let W be the width. \r\n" );
document.write( "\r\n" );
document.write( "Then the length is 4W and the height is 2W.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The total surface area is  2*(LW + LH + WH) = 2*( (4W)*W + (4W)*(2W) + W*(2W) ) = 2*(4W^2 + 8W^2 + 2W^2) = 28W^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus we have this equation to determine W\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    28W^2 = 198 in^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    W^2 = 198/28 =  = .\r\n" );
document.write( "\r\n" );
document.write( "    W            = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the dimensions are:  the length is  L = ;  the width  W = ;  the height  H = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The 3D diagonal of the solid is  D^2 = L^2 + W^2 + H^2 =  = ;   D =  =   in^2.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The volume is  LWH =  =   in^3.      ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Enjoy ( ! )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me for my teaching (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );