document.write( "Question 726739: A right rectangular prism with dimensions 2/3in. by 4/3in. by 8/3in. is enlarged by a scale factor of 1 1/2. \r
\n" ); document.write( "\n" ); document.write( "Q: The surface area of the original prism is ___ times as much as the surface area of the larger right rectangular prism. \n" ); document.write( "
Algebra.Com's Answer #444790 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
Such an evil problem! It's trying to trick us two ways.
\n" ); document.write( "The shoebox-like prism has a length, L, a width, W, and a height, H, that are all fractional quantities of inches.
\n" ); document.write( "However, those numbers do not matter, given the question at the end.
\n" ); document.write( "When you enlarge dimensions by a factor of \"x\",
\n" ); document.write( "the surface area of a solid changes by a factor of \"x%5E2\" and the volume by a factor of \"x%5E3\".
\n" ); document.write( "That happens because you have to multiply pairs of dimensions to get surface area, so when you multiply each pair, you get an \"x%5E2\" as a factor.
\n" ); document.write( "A face that had an area of \"LW\" gets it changed to \"%28Lx%29%28Wx%29=LWx%5E2\" .
\n" ); document.write( "A face that had an area of \"LH\" gets it changed to \"%28Lx%29%28Hx%29=LHx%5E2\" .
\n" ); document.write( "A face that had an area of \"HW\" gets it changed to \"%28Hx%29%28Wx%29=HWx%5E2\" .
\n" ); document.write( "
\n" ); document.write( "The scale factor was \"1%261%2F2=3%2F2\"
\n" ); document.write( "The dimensions of the large prism are \"3%2F2\" of the dimensions of the small one.
\n" ); document.write( "The dimensions of the small prism are \"2%2F3\"=\"1%2F%28%283%2F2%29%29\" of the dimensions of the large one.
\n" ); document.write( "\"%282%2F3%29%5E2=4%2F9\"
\n" ); document.write( "The surface area of the original (smaller) prism is \"highlight%284%2F9%29\" times as much as the surface area of the larger right rectangular prism. \n" ); document.write( "
\n" );