document.write( "Question 274404: Here's my problem...\r
\n" ); document.write( "\n" ); document.write( "A rectangular box is 4cm longer and 3cm narrower than a certain cube. The rectangular box and the cube have equal heights and equal surface areas. Find the length and width of the retangular box.\r
\n" ); document.write( "\n" ); document.write( "I am honestly at a loss on this one.\r
\n" ); document.write( "\n" ); document.write( "Thanks for your help! \n" ); document.write( "
Algebra.Com's Answer #200338 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Let's start with the cube.
\n" ); document.write( "Let x = the side (length, width and height) of the cube. The faces of the cube are all squares. The area of one of these squares is \"x%5E2\". There are 6 faces on a cube so the total surface area is \"6x%5E2\"

\n" ); document.write( "The box has the same height as the cube so the height is x. The box's length is 4 more than the length of the cube: x+4. The width of the box is 3 less than the cube's width: x-3. The surface area of a rectangular box is 2lw + 2lh + 2wh. With our length, width and height the surface area of our box is 2(x+4)(x-3) + 2(x+4)x + 2(x-3)x.

\n" ); document.write( "We are told that the surface areas of the cube and box are the same so:
\n" ); document.write( "\"6x%5E2+=+2%28x%2B4%29%28x-3%29+%2B+2%28x%2B4%29x+%2B+2%28x-3%29x\"
\n" ); document.write( "To solve this we start by simplifying:
\n" ); document.write( "\"6x%5E2+=+2%28x%5E2%2Bx-12%29+%2B+2%28x%5E2%2B4x%29+%2B+2%28x%5E2-3x%29\"
\n" ); document.write( "\"6x%5E2+=+2x%5E2%2Bx-24+%2B+2x%5E2%2B8x+%2B+2x%5E2-6x\"
\n" ); document.write( "\"6x%5E2+=+6x%5E2%2B3x-24\"
\n" ); document.write( "Now we want the variable on just one side so we'll subtract \"6x%5E2\" from each side:
\n" ); document.write( "\"0+=+3x-24\"
\n" ); document.write( "Add 24 to each side:
\n" ); document.write( "\"24+=+3x\"
\n" ); document.write( "Divide both sides by 3:
\n" ); document.write( "\"8+=+x\"
\n" ); document.write( "Since x = side of the cube (and the height of the box), this is not our answer. We are asked to find the width, x-3, and length, x+4. So the width is 5 and the length is 12. \n" ); document.write( "
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