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A photo is 4 inches longer than its width. A 3 inch border is placed around the photo making the total area around the photo and border 165 square inches. What are the dimensions of the photo?
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\n" ); document.write( "Let x = width of the photo
\n" ); document.write( "then
\n" ); document.write( "(x+4) = length of the photo
\n" ); document.write( ":
\n" ); document.write( "draw this out showing the 3\" border around the photo, label the photo width as
\n" ); document.write( "x and the length as (x+4), and you will see the dimensions of the rectangle
\n" ); document.write( " including the 3\" border are (x+6) by (x+4+6) or (x+10)
\n" ); document.write( ":
\n" ); document.write( "Overall area given as 165 sq/in so we have:
\n" ); document.write( "Length * width = 165 sq/in
\n" ); document.write( "(x+10)*(x+6) = 165
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + 6x + 10x + 60 = 165
\n" ); document.write( ":
\n" ); document.write( "x^2 + 16x + 60 - 165 = 0
\n" ); document.write( ":
\n" ); document.write( "x^2 + 16x - 105 = 0; our old friend, the quadratic equation!
\n" ); document.write( "Factors to
\n" ); document.write( "(x+21)(x-5) = 0
\n" ); document.write( "positive solution is what we want here:
\n" ); document.write( "x = 5\" is the width of the photo
\n" ); document.write( "and
\n" ); document.write( "5 + 4 = 9\" is the length
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\n" ); document.write( ";
\n" ); document.write( "Check solution by confirming the overall area:
\n" ); document.write( "(5+6)*(9+6) =
\n" ); document.write( "11 * 15 = 165 \n" ); document.write( "