document.write( "Question 1207821: An artist has 50 inches of oak trim to frame a painting. The frame is to have a border 3 inches wide surrounding the painting. \r
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\n" ); document.write( "\n" ); document.write( "(b) If the painting is rectangular with a length twice its width, what are the dimensions of the painting? What are the dimensions of the frame? \n" ); document.write( "

Algebra.Com's Answer #845940 by ikleyn(52866) $\"\"$ $\"About$

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document.write( "An artist has 50 inches of oak trim to frame a painting. \r\n" );
document.write( "The frame is to have a border 3 inches wide surrounding the painting.\r\n" );
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document.write( "(a) If the painting is square, what are its dimensions? \r\n" );
document.write( "    What are the dimensions of the frame?\r\n" );
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document.write( "(b) If the painting is rectangular with a length twice its width, what are \r\n" );
document.write( "    the dimensions of the painting? What are the dimensions of the frame?\r\n" );
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document.write( "(a)  Imagine this painting surrounded by 3 inches wide frame.\r\n" );
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document.write( "     Let x be size of the painting square, in inches.\r\n" );
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document.write( "     Then from the problem, you have this equation for x\r\n" );
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document.write( "          (x+3) + (x+3) + (x+3) + (x+3) = 50 inches,\r\n" );
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document.write( "     or\r\n" );
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document.write( "          4(x+3) = 50.\r\n" );
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document.write( "     It gives\r\n" );
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document.write( "          x+3 = 50/4 = 12.5 inches,\r\n" );
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document.write( "          x = 12.5 - 3 = 9.5 inches.\r\n" );
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document.write( "     Thus the dimensions of the painting are 9.5 by 9.5 inches.       <<<---===  Answer to (a).\r\n" );
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document.write( "     Outer dimensions of the frame are 9.5 + 3 + 3 = 15.5 inches.     <<<---===  Answer to (a).\r\n" );
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document.write( "(b)  Let w be the width of the painting, in inches.\r\n" );
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document.write( "     Then the length of the painting is 2x inches.\r\n" );
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document.write( "     From the problem, you have this equation for x\r\n" );
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document.write( "          (2w+3) + (w+3) + (2w+3) + (w+3) = 50 inches,\r\n" );
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document.write( "     or\r\n" );
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document.write( "          6w+12 = 50.\r\n" );
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document.write( "     It gives\r\n" );
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document.write( "          w = (50-12)/6 = 38/6 = 6 inches  (the width),\r\n" );
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document.write( "          2x= 12 inches                    (the length).\r\n" );
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document.write( "     Thus the dimensions of the painting are 6 inches by 12 inches.                           <<<---===  Answer to (b).\r\n" );
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document.write( "     Outer dimensions of the frame are 6 + 3 + 3 = 12  and  12 + 3 + 3 = 18  inches.     <<<---===  Answer to (b).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full.\r
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\n" ); document.write( "\n" ); document.write( "Be aware: both the solution method and the answers in the post by @mananth are incorrect.\r
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\n" ); document.write( "\n" ); document.write( "They are incorrect, because his setup equations are incorrect, in both cases.\r
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