document.write( "Question 565119: A rectangular picture 24 inches by 32 inches is surrounded by a border of uniform width. If the area of the border is 528 square inches less than the area of the picture, find the width of the border? \n" ); document.write( "

Algebra.Com's Answer #365664 by mananth(16946) $\"\"$ $\"About$

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Length of picture = 32
\n" ); document.write( "Width = 24
\n" ); document.write( "
\n" ); document.write( "Area = 768 In^2\r
\n" ); document.write( "\n" ); document.write( "Let the width of frame be x
\n" ); document.write( "..
\n" ); document.write( "Area = 768 In^2
\n" ); document.write( "Area of framework = 240 In^2
\n" ); document.write( "Length of picture+width =32+2x
\n" ); document.write( "width of picture+width= 24+2x
\n" ); document.write( "
\n" ); document.write( "(32+2x )(24+2x)-240= 768
\n" ); document.write( "
\n" ); document.write( "768+64x +48x+4x^2-240= 768
\n" ); document.write( "4X^2+112x-240= 0
\n" ); document.write( "Find the roots of the equation by quadratic formula
\n" ); document.write( " a= 4 b= 112 c= -240
\n" ); document.write( " b^2-4ac= 12544 + 3840
\n" ); document.write( " b^2-4ac= 16384
\n" ); document.write( " $\"sqrt%28%0916384%09%29\"$ = 128
\n" ); document.write( " $\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( " $\"x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( " x1=( -112 + 128 )/ 8
\n" ); document.write( " x1= 2
\n" ); document.write( " x2=( -112 -128 ) / 8
\n" ); document.write( " x2= -30
\n" ); document.write( " Ignore negative value \r
\n" ); document.write( "\n" ); document.write( "width = 2 inches \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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