document.write( "Question 175287: Sheila has a picture frame that measures 20cm by 30cm. If she puts a mat inside the frame that decreases the picture area by 264cm2, how wide is the mat? \n" ); document.write( "
Algebra.Com's Answer #130766 by ankor@dixie-net.com(22740)\"\" \"About 
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Sheila has a picture frame that measures 20cm by 30cm. If she puts a mat inside the frame that decreases the picture area by 264cm2, how wide is the mat?
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\n" ); document.write( "Let x = the width of the matte around the picture
\n" ); document.write( "Then
\n" ); document.write( "Picture area: (20-2x) * (30-2x) = (600 - 100x + 4x^2) sq/cm
\n" ); document.write( "Overall frame area = 20 * 30 = 600 sq/c
\n" ); document.write( ":
\n" ); document.write( "Frame area - picture area = 264
\n" ); document.write( "600 - (600 - 100x + 4x^2) = 264
\n" ); document.write( ":
\n" ); document.write( "600 - 600 + 100x - 4x^2 = 264
\n" ); document.write( ":
\n" ); document.write( "0 = 4x^2 - 100x + 264
\n" ); document.write( "Simplify, divide eq by 4
\n" ); document.write( "x^2 - 25x + 66 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(x-22)(x-3) = 0
\n" ); document.write( "Two solutions:
\n" ); document.write( "x = 22 cm
\n" ); document.write( "and
\n" ); document.write( "x = 3 cm, this is the one that makes sense
\n" ); document.write( ":
\n" ); document.write( "Check solution (subtract 2x which is 6 cm from the frame dimensions):
\n" ); document.write( "(20*30) - (14*24) =
\n" ); document.write( "600 - 336 = 264
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