document.write( "Question 130098: A picture is 10cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 5cm border on all sides. If the area of the border is alone 580cm squared, what are the the dimensions of the picture? \n" ); document.write( "

Algebra.Com's Answer #95053 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"x\"$ = the width
\n" ); document.write( "The height will be $\"x+%2B+10\"$
\n" ); document.write( "The area of the picture is then $\"x%2A%28x+%2B+10%29\"$
\n" ); document.write( "Including the border, the width is $\"x+%2B+5+%2B+5\"$
\n" ); document.write( "Including the border, the height is $\"x+%2B+10+%2B+5+%2B+5\"$
\n" ); document.write( " $\"%28x+%2B+5+%2B+5%29%28x+%2B+10+%2B+5+%2B+5%29+=+580+%2B+x%2A%28x+%2B+10%29\"$
\n" ); document.write( " $\"%28x+%2B+10%29%28x+%2B+20%29+=+580+%2B+x%5E2+%2B+10x\"$
\n" ); document.write( " $\"x%5E2+%2B+30x+%2B+200+=+580+%2B+x%5E2+%2B+10x\"$
\n" ); document.write( " $\"20x+=+580+-+200\"$
\n" ); document.write( " $\"x+=+19\"$
\n" ); document.write( " $\"x+%2B+10+=+29\"$
\n" ); document.write( "The dimensions of the picture are 19 x 29
\n" ); document.write( "check answer:
\n" ); document.write( "Adding up the pieces of the border,
\n" ); document.write( " $\"580+=+2%2A5%2A19+%2B+2%2A5%2A29+%2B+4%2A5%5E2\"$
\n" ); document.write( " $\"580+=+190+%2B+290+%2B+100\"$
\n" ); document.write( " $\"580+=+580\"$
\n" ); document.write( "OK
\n" ); document.write( "The area of the border + picture is
\n" ); document.write( " $\"19+%2B+5+%2B+5%29%2829+%2B+5+%2B+5%29\"$
\n" ); document.write( " $\"29%2A39+=+1131\"$
\n" ); document.write( " $\"1131+-+580+=+551\"$
\n" ); document.write( " $\"19%2A29+=+551\"$
\n" ); document.write( "OK \n" ); document.write( "

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